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PREFACE 



The science of Astronomy, conversant as it is with tt»«» 
Bublimest natural phenomena, has ever engaged the attention 
of mankind, even when, from century to century, scarcely any 
new revelation of the skies rewarded the labors of the 
astronomer. 

But at the jrssent time, when discovery crowds upon dis- 
covery, and the whole field of astronomical research has been 
wonderfully enlarged, it has suddenly become invested with 
the charms and freshness of a new science ; and all classes of 
society listen with wonder and delight to the recital of the 
lofty truths and amazing facts which it unfolds. 

In attempting, therefore, with many honored names, to 
cause Astronomy to descend from the dignified seclusion of 
the observatory, that she may walk as a familiar guest amid 
the lesser temples of knowledge, no apology is required for the 
motive that prompts the task how much soever it may be 
needed on account of the execution. 

In the present treatise the author has not sought to adapt its 
subject to the youthful mind, by curtailing the science of its 
fair proportions, and omitting every thing that requires patient 
and earnest study ; but he has aimed to preserve its great princi- 
ples and facts in their integrity, and so to arrange, explain, and 
illustrate them, that they may stand out boldly defined, and 
be clear and intelligible to the honest and faithful student, — 
this is all that can be done for a pupil, if a science is to be 
taught in its completeness and not in parts. 



K 



IV PREFACE. 

The hill of science will always be a hill. Impeding ts and ob- 
structions may be removed and the ascent rendered easier, but 
the hill cannot be leveled, it must be surmounted. 

Several peculiarities are contained in this text-book, which it 
te thought will be of material service to the pupil in obtaining 
a knowledge o/ iLe science. The most important of these we 
shall now briefly nonce. 

I. It is usual, in most text-books on this science, to explain 
many astronomical phenomena by the apparent, and not by 
the real motions of the celestial bodies. In this treatise the 
opposite course is taken, wherever practicable ; the explanations 
being based upon the real motions of the heavenly bodies. By 
pursuing this method, the subsequent acquisitions of the scholar 
are built upon the truth itself, and not upon what appears to be 
true. 

II. The mode of ascertaining the distances and magnitudes 
of the heavenly bodies is so simplified that any student, who 
understands the rule of proportion, can readily comprehend it. 

III. Scientific terms and expressions are explained by foot 
notes on the pages in which they occur ; and in these notes are 
likewise embodied such illustrations and information as tend 
to elucidate the text. 

In the preparation of this manual, the author has had re- 
course to numerous standard works upon Astronomy, and has 
brought up the subject to the present time. For information 
respecting recent astronomical discoveries, he is especially in- 
debted to the treatises of Sir John Hersohel and Mr. J 
Russel Hind. 

Hartyord, Feb. 19 th, 1855 



PREFACE 

TO THE LAST REVISED EDITION. 



During the last few years the progress of Astronomy has 
been very rapid ; for the number of known planetoids has 
been greatly increased, and a new value assigned to the solar 
parallax, which involves changes in the elements of the 
heavenly bodies running throughout the Solar System, and 
extending even to the fixed stars. 

Within this period is also embraced the wondrous dis- 
coveries due to the spectrum analysis, which have revealed 
to us, to some extent, not only the physical nature of the 
sun and planets, but also that of comets, fixed stars, nebulae, 
and meteoric bodies. 

It has been the aim of the author in this edition, to bring 
the work fully up to the present (1870) state of the science. 
The chapter on the sun has been entirely rewritten, and many 
other changes made which the advance of Astronomy de- 
manded. New subjects have also been added, as for instance 
the nature of Meteorites and Shooting-stars, a description of 
the principal Constellations, and a History of Astronomy. 
Hartford, Conn., July, 1870. 



CONTENTS. 



I'age. 

Preface,.. « 2 

Preface to the last revised edition, 4 



INTRODUCTORY CHAPTER. 



Astronomy defined, 13 

Solar system, 14 

Interior Planets, 14 

Asteroids, 14 



Exterior Planets, 14 

Symbols of the Planets 14 

Mode of conducting astronomical in- 
vestigations, 15 



EXPLANATORY CHAPTER. 



Angle, 17 

Right angle,. 18 

Triangles,. 19 

Similar triangles, 19 

A plane surface,. 20 

A plane figure, 20 j 



An ellipse 20 

To construct an ellipse, 21 

Eccentricity , 21 

A sphere, 22 

Poles of a circle of a sphere, 22 



PART FIRST. 



THE EARTH IN ITS RELATION TO OTHER HEAVENLY BODIES. 

ClIAPTEli I. 



ITS FORM, SIZE, ROTATION, AND DENSITY. 



The form of the earth, 24 

Its size, 26 

Its rotation, 29 



Deviation of falling bodies from a 

vertical line, 31 

Variation in the weight of bodies,. . . 32 

Density 33 



CHAPTER II. 

THE HORIZON. 



Sensible horizon, 33 

Rational horizon, 34 

Plane of the horizon not fixed in 

space, 35 

Zenith and Nadir, 36 

Changing aspect of the heavens aris- 
ing from the rotation of the earth, 36 
Why the stars appear to describe cir- 
cles...... 38 



Why these circles differ in size, 38 

Changing aspect of the heavens aris- 
ing from change in latitude, 39 

Circle of perpetual apparition, 41 

Circle of perpetuaUoccultation,. ... 42 
Latitude of any place equal to the 
elevation of the pole of the heav- 
ens, 45 



VI 



CONTENTS. 



ON' 



CHAPTER in. 

MODE OF DETERMINING THE PLACE OF A HEAVENLY BODY. 



Celestial sphere, poles, axes, and 

meridians, 46 

Equators, 48 

Vertical circles, 49 

The position of a star how deter- 
mined, 49 



Page. 
Azimuth, amplitude, altitude, and 

zenith distance, 50 

Declination and right ascension,. ... 51 

Ecliptic, 53 

Latitude and longitude, 63 

The signs, 54 

Zodiac, 54 



CHAPTER IV. 
OF REFRACTION AND PARALLAX. 



Refraction, 55 

Variation of refraction in respect to 
altitude, 66 

The effect of refraction on the posi- 
tion of heavenly bodies, 58 

Its effect on their declination and 
right ascension, 58 

Refraction influenced by the tem- 
perature and pressure of the at- 
mosphere, 60 

Of parallax, 60 



Parallax — how measured, 62 

Variation in parallax — effect of alti- 
tude, 63 

Horizontal parallax, 63 

Effect of distance, 63 

Effect of parallax upon the true po- 
sition of a heavenly body , 64 

Its effect on right ascension and de- 
clination, 64 

Parallax — its value, 65 



Transit instrument, 

Time occupied by the earth in per- 
forming one rotation — how deter- 
mined, 

Standard unit of time, 

Of the sidereal and solar day, 

Inequality in the length of the solar 
days, 



CHAPTER V. 

OF THE MEASUREMENT OF TIME. 

66 



Modes of reckoning time, 77 

Apparent time, 78 

Mean solar time, 78 

Astronomical time, 78 

Equation of time, 79 

Astronomical clock — sidereal time — 

error and rate, 80 

Right ascension — how determined,. . 81 



CHAPTER VI. 

OF THE ANNUAL MOTION OF THE EARTH. 



Sun's apparent motion in declina- 
tion, 81 

Sun's apparent motion in right as- 
cension, 82 

Sun's apparent path 83 



Sun's apparent motion in declina- 
tion explained, 

Sun's apparent motion in right as- 
cension explained, 

Direction of motion in space explain- 
ed, 



S3 



86 



CHAPTER VII. 

OF THE YEAR. 



Tropical year defined , 87 

Its length — how found, 87 

The calendar, 89 

Sothic period, 90 

The Mexican year, 90 



The christian calendar— Julian cor- 
rection, 91 

Gregorian correction 91 

Gregorian rule,. 93 



CHAPTER VIII. 

OF THE PRECESSION OF THE EQUINOXES, — CHANGE OF THE POLE-STAR, AND NUTATION. 



Of the precession of the equinoxes , . . 93 

Sidereal year, 96 

Change of the pole-star, 97 



Effect of precession on the right as- 
cension and longitude of the stars, 98 



CONTENTS. 



Vll 



Page. 

Its effect on the declination and lati- 
tude, 98 

Terrestrial latitude constant, 98 

Relative positions of the signs and 
constellation of the zodiac variable, 99 

Cause op the precession, 100 



Page. 

Influence of the sun, 100 

Influence of the moon and planets,. 101 

Nutation, 101 

Obliquity of the ecliptic affected by 
nutation, 103 



CHAPTER IX. 

OF THE EARTH'S ORBIT. 



Sun's apparent diameter 105 

Anomalistic year, 107 

Apparent angular motion, 108 

Variation in the earth's orbital ve- 
locity, 109 

Form of the earth's orbit ascertain- 
ed by angular velocities, 110 



Product of the square of the dis- 
tance into the angular velocity — 

constant 110 

Kepler's laws, 112 

Extent of the earth's orbit, 112 

How ascertained, 112 



CHAPTER X. 

OP THE SEASONS. 



The seasons, 115 

Spring, 118 

Summer, 118 

Autumn, 120 

Winter, 120 

Polar winter — effects of refraction,. 121 

Twilight and its influence, 122 



The cause of the unequal distribu- 
tion of heat over the surface of 
the globe, 123 

The summer of the southern hemis- 
phere not hotter than that of the 
northern, 124 



PART SECOND. 

SOLAR SYSTEM, 

CHAPTER I. 



Real diameter of the sun,. 



.. 126 

.. 127 

Mass and Density, 128 

Force of gravity at the sun, 128 

Solar surface— general appearance , . 128 

Nature of the spots, 128 

Their extent, number, and period- 
icity, 129 

Their position, 130 

Apparent motion of the spots, 131 

Their proper motion, 132 

Faculae, 133 

Pores j granules, and willow leaves,. 133 

Rotation of the sun on it3 axis, 131 

Inclination of the sun's equator to 

the plane of the ecliptic, 137 



SUN. 

Nature of the sun, 138 

Spectrum analysis, 138 

Spectra of flames containing metallic 

and other vapors— bright lines,. . 138 
Experiments of Bunsen and Kirch- 

off, 139 

Dark lines — how caused, 139 

Metals found in the sun, 140 

Physical constitution of the sun,. . 140 

Photosphere, 141 

Exterior atmosphere or chromos- 
phere,. . : 141 

Cause of the spots, 142 

Nature of the faculae,. 142 

Solar disturbances — their influence 

on the magnetism of the earth,. . 143 



CHAPTER II. 

THE MOON. 



The distance of the moon, 143 

Diameter in miles, 144 

Moon's phases, 146 

From new moon to the first quarter, 146 
From the first quarter to full moon, 14" 
From full moon to the third quar- 
ter 147 



From the third quarter to new 

moon, 147 

What the phases prove 150 

Sidereal month, 150 

Physical aspects of the moon,. . . , 152 

Lunar mountains, 153 

The heights measured, , . 164 



Vlll 



CONTENTS. 



Page. 
Names and heights of the lunar 

mountains, 156 

Lunar craters, 157 

Lunar volcanoes, 159 

Lunar atmosphere, 160 

Lunar heat, 161 

The bulk, mass, and density of the 

moon, 161 

Moon's orbit, 161 

Its figure determined, 162 

Plane of the moon's orbit, 162 

The line of the nodes, 163 

The line of the apsides, 164 



Page 
Increased apparent si* of the moon 

when in the zenith, 165 

The moon always turns the same 

face toward the earth, 166 

Libration in longitude, 167 

Libration in latitude, 168 

Diurnal libration 169 

Length of the lunar day, 169 

The appearance of the earth as seen 

from the moon , 170 

Acceleration of the moon's motion 

in her orbit, 171 

The moon's path in space, 172 



CHAPTER III. 



ECLIPSES OF THE SUN AND MOON. 



Lunar eclipses, 173 

Of the earth's shadow, 175 

Extent of shadow traversed by the 

moon, 177 

Of the penumbra, 177 

Duration of a lunar eclipse, 173 

Red light of the disk, 179 

Earliest observations of lunar eclip- 
ses, 180 

Eclipses of the sun, 180 

Porm of a solar eclipse, 180 



Shadow of the moon, 181 

Altitude of the moon, — its effect on 

eclipses, 182 

Total eclipses of the sun, 184 

Duration of a solar eclipse, 186 

Solar and lunar eclipses — points of 

difference, 186 

Frequency of eclipses, 187 

Quantity of an eclipse,. 187 

The period of the eclipses— the Saros, 189 



CHAPTER IV. 

CENTRAL FORCES AND GRAVITATION. 



Of gravity, 192 I Universal gravitation discovered,. . . 194 

Its variation, 193 | Universal gravitation defined, 197 

CHAPTER V. 



the planets. 



Table of the elements of the planets, 193 

Their distances, 198 

Kepler's law of distances, 200 

Bode's law of distances, 201 

Of their magnitudes, 201 

Division of the planets with reference 

to the earth 202 

Inferior planets, 202 

Mercury, 203 

His solar distance, 203 

Orbit— inclination of its plane, 204 

Size — apparent — real, 204 

Periodic time, 205 

Rotation on its axis, 205 

Phases, 206 

Transit of Mercury, 206 

Splendor of Mercury , 207 

Mass and Density, 208 

Ancient observations of Mercury, .. . 209 

Venus, 209 

Distance and periodic time, 209 

Apparent diameter, 209 

Rotation, 210 

Orbit — Inclination of its plane to that 

of the ecliptic, 211 

Phases 211 



Splendor of Venus, 212 

Mass and density, 214 

Atmosphere of Venus, 214 

Transit of Venus, 214 

Value of the solar parallax, 217 

The Earth, 217 

Superior planets, 217 

Mars, 218 

Distance— Orbit — Inclination of the 

plane of the orbit, 218 

Real and apparent diameter, 218 

Phases, 219 

Physical aspect — Atmosphere, 220 

Rotation, — Inclination of the axis, 

Ellipticity, 221 

Density and mass, 221 

Intensity of solar light, 222 

THE ASTEROIDS, 222 

Ceres 224 

Pallas, 225 

Juno, 225 

Vesta, 226 

Later discoveries, 228 

Peculiarities of the Asteroids, 229 

Their size, 229 

Obliquity and eccentricity 229 



CONTENTS. 



IX 



Page. 
Orbits 229 

Probable number of the Asteroids,. . 229 

Origin of the Asteroids, 230 

Jupiter, 231 

Periodic time — distance, 231 

Diameter — apparent — real, 231 

Ellipticity— bulk, 231 

Physical aspect of Jupiter— Belts, . . 231 

Rotation, 232 

Velocity or rotation 233 

Mass— Density 233 

Satellites of Jupiter— their discovery, 233 
Their magnitudes, diameters, dis- 
tances, and periods of revolution,. 234 
Kepler's laws— applicable to the sat- 
ellites — their rotation, 234 

Transits and eclipses of the satellites, 235 

Velocity of light, 236 

Saturn 287 

Distance — Periodical revolution and 

inclination of orbit, 238 

Form— diameter, 238 

Bulk, diameter, intensity of light, . 238 

Physical aspect — atmosphere, 238 

Rotation and inclination of its axis,. 239 

Ring of Saturn— its discovery, 239 

Form — constitution, 240 

Rotation — Position— Inclination to 

the ecliptic,. 240 

Phases of the ring, 241 

Vanishing of the ring— Three causes, 242 
Divisions of the ring,. 243 



Page. 

Dimensions of the rings,. 244 

Satellites op Saturn, 245 

Mimas, 245 

Enceladus, 245 

Tethys 245 

Dione, '. 246 

Rhea, 246 

Titan, 246 

Hyperion, 247 

Japetus, 247 

Diameter of the satellites, 247 

Ancient observations of Saturn, 247 

Uranus or Herschel, 248 

Aspect— Diameter— Mass— Density, . 248 

Rotation , 248 

Distance — Inclination of Orbit — Pe- 
riodic time, 249 

Satellites of Uranus, 249 

intensity of light, 250 

Neptune, 250 

History of its discovery , 250 

Name, — Diameter, — Mass, — Density, 251 
Orbit, — Inclination of orbit, — Dis- 
tance, — Periodic time, 251 

Intensity of light, 251 

Has Neptune a ring, 251 

The satellite of Neptune, 252 

Real and apparent motions of the 

planets, .'. 252 

Causes of the apparent motions, 263 

Apparent motions explained, 253 

The planets at times stationary,. ... 254 



CHAPTER VI. 

COMETS. 



Their constitution, 254 

Number of comets,. 255 

Splendor and siie, 257 

Velocity, 257 

Temperature, 258 

Comets shine by reflected light, 258 

Orbits, — Perihelion distances, 269 

Inclination of the orbits,— Direction 

of motion, 260 

Elements,— Identity 260 



Halley's comet, 261 

Encke's comet, 262 

Biela's comet, 262 

Faye's comet, 263 

D 1 Arrest's comet, 263 

Wennecke's comet, 263 

Comet of 1680, 263 

Comet of 1843,.... 264 

Physical nature of comets, 265 

Collision with the earth, 265 



CHAPTER VII. 

METEORIC BODIES. 



Shooting stars, 266 

Height and Velocity, 266 

How they are inflamed, 268 

Meteoric showers, 268 

Meteorites,. . . 270 

Weston meteorite 270 

Ohio meteorite, 271 

Height and velocity of meteorites,. . 271 



Size of meteorites 271 

Aerolites, .... . . ........ .......... . 272 

Meteoric iron, 272 

Theory of meteoric bodies 273 

November stream, 273 

August ring, 273 

Meteoric Phenomena, 274 



CHAPTER VIII. 

TIDES. 

Tides defined, 274 | Why high tides occur on opposite 

Cause of the tides 276 | sides of the globe, 276 



CONTENTS. 



Page. 
Why low tides occur on opposite 

sides of the globe 277 

Solar influence 278 

Spring and neap tides, 279 

Time of the tide, 281 

Priming or lagging of the tide, 282 

Effect of declination on the height 

of the tide, 282 



Page. 

Actual heights of the tide, 283 

Derivative tides, 284 

Nature and velocity of the tide wave, 284 

Cotidal lines, 284 

Tides in| lakes, and seas connected 
with the ocean, 285 



CHAPTER IX. 

TERRESTRIAL LONGITUDE. 

Longitude ascertained by four meth- I By eclipses, 287 

ods 286 By the electric telegraph, 288 

By chronometers 286 | By the lunar method 288 



PART III. 



THE STARRY HEAVENS. 

CHAPTER I. 

OP THE FIXED STARS IN GENERAL AND THE CONSTELLATIONS. 



The fixed stars, 290 

Magnitudes, • 290 

Number of stars, 291 

Distance of the fixed stars, 292 

Parallax and distance of Alpha 

Centauri 293 

Parallax and distance of 61 Cygni, . . 294 
Nature and intrinsic splendor of the 

fixed stars, 294 

The constellations, 295 



The stars in the constellations, — 

How designated, 295 

Conspicuous constellations described, 296 

Principal constellations, 297 

Constellations north of the zodiac,.. . 298 

Constellations of the zodiac, 298 

Constellations south of the zodiac,. . 298 

The celestial globe, 298 

Star maps, 300 



Periodical stars, 

Mira, 

Algol, 

Temporary stars 
Double stars, 



CHAPTER II. 

DIFFERENT KINDS OF STARS,— STELLAR MOTIONS,— BINARY SYSTEMS. 

Examples, 305 

Number of double and multiple 

stars,. 305 

Stellar motions, 306 

Motion of the solar system, 306 

Proper motion of the stars, 306 

Central sun,. 307 

Binary stars, 308 

Orbits,— Periodic times, 308 



301 
301 
301 
304 



Castor, — Alpha Centauri, — 61 Cygni, 304 

Colored double stars, 304 

Triple, and quadruple or multiple 
stars 305 



CHAPTER m. 

STARRY CLUSTERS,— NEBULB,— NEBULOUS STARS,— ZODIACAL LIGHT,— MAGELLAN 
CLOUDS,— STRUCTURE OF THE HEAVENS. 



Starry clusters, 309 

Number of stars in a cluster, 310 

Milky Way of Galaxy, 310 

Nebulae, 311 

Elliptical nebulae, 312 

Annular nebulae, 312 

Planetary nebulae, 312 

Double nebulae, 313 

Spiral nebulae, 313 

Irregular nebulae, 313 

Their constitution 314 



Revelations of the spectrum, 316 

Number and distance of stellar clus- 
ters and nebulae, 316 

Their physical structure, 316 

Nebulous stars, 817 

Zodiacal light, 318 

Aspects, 318 



Size, 



318 



Nature, 318 

Magellan clouds, 319 

The nebular hypothesis 319 



CONTENTS. 



XI 



Page. 

The hypothesis stated, 319 

Nebulous zone changed into planets, 320 

Secondary rings and moons, 321 

Physical condition of the bodies of 
the system, 321 



Page. 

Coincidences existing between the 
hypothetical nebular, system and 
the solar system,. 321 

Origin of the fixed stars, 322 



PART IV. 



SOGiART OF THE HISTORY OP ASTBONOMY. 



Ancient astronomy, 323 

Chinese astronomy, 323 

Egyptian astronomy, 323 

Chaldean astronomy, 324 

Hindoo astronomy, 325 

Greek astronomy, 325 

Alexandrian school, 327 

Hipparchus, 327 

Ptolemy, 328 

Ptolemaic system, 328 

The system central, 329 



Arabian astronomy, 

Persian astronomy, 

Tartar astronomy, 

Modern astronomy, 

Copernican system, 

Tycho Brahe, 

Tychonic system, 

Progress of astronomy under Kepler, 

Galileo and others, 

Newton, Holley, and Bradley, 

Recent progress of astronomy, 



329 



330 
331 

381 



332 

333 



Astronomical problems,. 



335 



APPENDIX 



Rotation of the earth proved by the I Density of the earth, 347 

pendulum, 346 | Table of known planetoids, 350 



ASTRONOMY, 



INTRODUCTORY CHAPTER. 

1. Astronomy is that branch of Natural Science 
which treats of the magnitudes, distances, constitu- 
tions, and motions of the Heavenly Bodies, and the 
laws which regulate them. 

2. The Heavenly Bodies consist of moons, planets, 1 
meteoric bodies, comets, 2 and suns ; and possibly a fifth 
class exists, called nebulce. 3 To moons, planets, and 
suns the general name of stars is often given. 

3. No heavenly body is independent of another. 
Each exists and moves as a part of one vast and har- 
monious combination, termed the Universe. The Vis- 
ible Heavens are a portion of this Universe. How 
great or how small a portion we cannot say ; for the 
rest, shrouded from our view in the depths of space, 
lies beyond the limits of our knowledge. 

The mode of union existing among the heavenly 
bodies is the following : One or more moons revolve 
about a planet ; several planets with their attendant 
moons revolve about a sun, around which, likewise, 
sweeps a numerous train of comets. A sun with its 
assemblage of planets and comets constitutes a system. 

The investigations of astronomers tend to prove 
that these systems are not fixed in space, but revolve 

1. Planet, from the Greek word planetes, signifying a wanderer, a star 
that changes its place in the heavens. 

2. Comet, from the Latin word coma, a head of hair, this body present 
ing a hairy appearance. 

3. The name of nebula is given by astronomers to certain objects in the 
distant heavens which appear like small clouds, or specks of mist. True 
nebulae are supposed to be vast collections of unformed matter, thinly 
diffused through space. Nebulae is a' Latin word, signifying mists, or 
clouds. 

What is Astronomy ? What do the heavenly bodies consist ofl Does a heavenly 
oody exist and move independent of others? What is said of the visible hemer!* 1 
What is the mode of union between henvenlv bodies* J 



14 ASTEONOMY. 

like planets about some common central point, or body. 
And we have reason for believing that this mode of ar- 
rangement extends throughout all space, groups of sys- 
tems rising one above the other in magnitude ; the 
lesser forming a part of a greater, until at length their 
vast aggregate embraces and completes the Universe. 

4. Solar System. The sun with his train of plan- 
ets, moons, meteoric bodies and comets, forms the 
Solar System. 

The number of planets now known (1870) is one 
hundred and eight Of these, one hundred and 

six have been discovered within the last twenty-five 
years, and others will doubtless be detected. The 
planets form three natural groups, viz, the Interior 
planets, the Asteroids, 1 and the Exterior planets, 
which are distinguished from one another by marked 
peculiarities. 

5. Interior Planets. The interior planets are 
nearest to the sun, and comprise, in the order of their 
solar distances, Mercury, Venus, Earth, and Mars. 
These bodies all revolve on their axes in about 24 
hours, have but one moon, and are of large size, their 
diameters varying from about 3,000 to 8,000 miles. 

6. Asteroids. Beyond Mars are numerous plane- 
tary bodies termed asteroids. They are of exceed- 
ingly small dimensions, are clustered together, and 
their interlocked orbits form a complex ring. One 
hundred and nine have at present been discovered, 
the names of which in full will be given hereafter. 

7. Exterior Planets. Outside of the asteroids are 
the exterior planets, consisting of Jupiter, Saturn, 
Uranus, and Neptune. The members of this system 
far surpass in size those of the interior group ; they 
are all attended by moons, and the period of their 
axial rotations, as far as determined, is about 10 hours. 

8. Symbols of the Planets. The interior and ex- 
terior planets, and the four earliest discovered aster- 
oids, are represented by certain symbols, as follows : 

1. Asteroids. From two Greek words, aster, a star, and eidos, like. 
Like a star, because all these planets are very small. 

Describe the solar system. What is said respecting the number of the planets? 
How are they grouped ? State the peculiarities of the three groups. 



NAMES. 

MERCURY, 


SYMBOLS 

<5 


VENUS, 


9 


EARTH, 


fB 


MARS, 


c? 


JUPITER, 


% 


SATURN, 


h 


HERSCHEL, 


or m\ 


URANUS, 


NEPTUNE, 


? 


CERES, 


2 


PALLAS, 





JUNO, 





VESTA, 


a 



INTRODUCTORY CHAPTER. 15 



a wand. 

a mirror. 

a circle with the equator and a meridian. 

a shield and spear. 

the hieroglyphic of an eagle. 

an ancient scythe. 

the initial letter of Herschel, with a planet 

pendent, 
a trident, 
a sickle. 
a lance head. 

a sceptre crowned by a star. 
a flame burning on an altar. 

The asteroids are, in general, designated by circles 
enclosing a number, which indicates the position of 
the asteroid to which it is affixed in the order of dis- 
covery. Thus bellona (as) shows that twenty-seven 
asteroids were discovered before Bellona. 

In the annexed cut a view of the solar system is 
presented. The Roman numeral, I, represents the 
orbit 1 of Mercury ; II, that of Yenus ; III, that of the 
Earth ; IY, that of Mars ; Y, the orbit of the nearest 
asteroid ; VI, that of the most remote asteroid ; VII, 
is the orbit of Jupiter ; VIII, of Saturn ; IX, of Her- 
schel ; and X, of Neptune. In the cut, the distances 
of the several planets from the sun bear the same re- 
lation to each other as their actual distances. 

9. The Mode of Conducting Astronomical In- 
vestigations. When an artisan wishes to ascertain 
the dimensions of a stick of timber he does so by means 
of a rule, the length of which he knows, and thus he 
obtains the solidity of the log in feet and inches. 

When, likewise, we wish to determine the speed of a 
locomotive, we measure by the aid of a watch the time 
taken to pass over a known number of miles. Thus un- 
known magnitudes and motions are ascertained by com- 
paring them with such as are known. 

In astronomical investigations we pursue a like course, 
and begin with determining the size, motions, and jt>r?^ 
of the Earth, with other important particulars that are 
within our reach. We thus obtain fixed standards of 

1 . Orbit means the path of a planet about the sun. So called from 
the Latin word orbis, a circle, a circuit. 

"Describe the Symbols of the planets. Explain the figure. In what manner are 
astronomical investigations conducted ? 




SOLAR FYSTE.M. 



EXPLANATORY CHAPTER. 17 

measurement, whereby we are enabled to push our in- 
quiries beyond the earth, and to compute the distances, 
times, motions, and velocities of many of the bright orbs 1 
that glitter about us, and the extent of the vast spaces 
through which they move. In the study of Astronomy 
our attention is, therefore, directed First to the Earth in 
its relation to the rest of the heavenly bodies. Secondly, 
to the Solar System. Thirdly, to the Starry Heav 
ens, of which this system is a part. 



EXPLANATORY CHAPTER. 



10. In learning Astronomy it is necessary for the 
pupil at the outset to know the meaning of certain 
mathematical and philosophical terms and expressions, 
which are constantly occurring in the discussion of as- 
tronomical subjects. These must be mastered in order 
to obtain a clear understanding of the science, and yet 
they are by no means difficult to comprehend. The 
most important of these are explained in the present 
chapter. The meaning of other terms and phrases will 
be given as they occur in the book. 

11. Angle. An angle is the opening or inclination 
between two lines that meet each other ; thus, in Fig % the 



FIR. 2. 




AN ANGLE. 



1. TTie stars are frequently called orbs, from their round figures. OrAi*, 
(Latin.) a circle. 



In what order are the subjects of astronomy to be studied ? In learning fcSfronom? 
u-hat is it ner^ssary for the pupil to do at the outset ? What is an angle 1 

o* 



18 ASTRONOMY. 

line AB meets the line BO, and the opening between 
them is called the angle, B, or the angle, ABC ; the letter 
at the point of meeting, always being placed in the 
naiddle. 

The size of an angle is computed as follows. The 
circumference of any circle being divided into 360 equal 
parts, each part is called a degree; a degree being divided 
into 60 equal parts, each part is called a minute ; a min- 
ute being divided into 60 equal parts, each part is called 
a second. If, now, we take the point B, as the centre of 
a circle, and describe the circumference, DEF, cutting the 
two lines, AB and CB in any two points, as E and F, the 
number of degrees, minutes, and seconds contained in the 
part of the circumference, EF, included between the 
two lines, AB and CB, gives the value of the angle, 
ABC. For example, if the length of the circumfer- 
ence, DEF, was 360 inches, and the part, EF, contained 
40 inches and nine-sixtieths (40eV) of an inch, ABC 
would be an angle of forty degrees and nine minutes 
(40° 9 / .) Degrees are denoted by the following char- 
acter, ° ; minutes thus, ' ; and seconds thus, ". 

12. A Eight Angle. A right angle contains 90°, 
and can be thus constructed. Draw two diameters 
through any circle, dividing the circumference into four 
equal' parts, and each of the angles at the centre will be 
a right angle, for since the whole circumference contains 
three hundred and sixty degrees, one-fourth of it con- 

FIG. 3 




RIGHT ANGLE. 



How is its size computed 1 Describe from the figure. How are degrees, minutes, ana 
seconds denoted 1 What is a right angle, and how is it constructed 1 



EXPLANATORY CHAPTER. 



19 



lams ninety degrees. Thus, in Fig. 3, the two diame- 
ters, AB and DE, dividing the circumference of the circle, 
A, D, B, E, into four equal parts, make each of the an- 
gles at the centre, right angles, viz., ACD. DCB, BCE, 
and ECA. 

13. Triangles. A triangle is a figure that is bounded 
by three lines, either curved or straight, and contains three 
angles; hence its name, derived in part from a Latin word, 



FIG 4 



FIG. 5 





A RECTILINEAR TRIANGLE. A RECTILINEAR RIGHT-ANGLED TRIANGLE. 

tres, meaning three. The sum of the three angles of any 
rectilinear 1 triangle is always equal to 180°. Fig. 4 rep- 
resents any such triangle, and the sum of its angles is 
equal to 180° A right-angled rectiliDear triangle is one 
that contains one right angle. Thus, Fig. 5 is a right- 
angled triangle, since it contains a right angle, viz., ABC. 
14. Similar Triangles. Similar triangles are those 
which have all the angles of one triangle equal to those of 



FIG. 6. 



FIG 7. 




SIMILAR TRIANGLES. 



the other, each to each, and the sides forming the equal an. 
gees proportional ; thus, in Figs. 6 and 7, the triangles 

1. Rectilinear, from rectus, straight, and linea, a line, (Latin,) straight 
lined. 



What is a triangle ? How many degrees does it contain 1 Refer to figure. What ii 
a right-angled triangle ? Refer to figure. What are similar triangles? Explain from 
figure. 



20 ASTRONOMY. 

AVB l C l and ABC, are similar, because the angle B 1 
equals B, A 1 equals A, C 1 equals C, and the side A l B l : 
AB : : A l G l : AQ\ and so of the other sides. 

15. A Plane Surface. A plane surface is such that if 
any two points in the surface are connected by a straight 
line, every part of that straight line touches the surface. 
To illustrate. The surface of tranquil water in a pond 
is a plane surface, because if any two points on the sur- 
face are taken, and are connected by a perfectly straight 
rod, every part of the lower side of the rod touches the 
water. Such a surface is sometimes termed a fidane. 
Thus, the surface of this page, when pressed flat| is a 
plane surface, or plane. 

15 l . A Plane Figure. A plane figure is one whose 
bounding line or lines are situated in the same plane. 
The flat cover of this book is a plane figure. 

16. Ellipse. An ellipse is a plane figure, bounded 
by a curved line; and so constructed that if two straight 
lines are drawn from two points within, called the foci, to 
any point in the curve, the sum of these lines is inva- 
riably the same for the same ellipse. Thus, the an- 
nexed figure is an ellipse. F and F l , the foci, and if 



FIG 


3 











AN ELLIPSE. 



straight lines are drawn to any points, as M and M 1 ; 
FU added to F l M equals FM l added to F l M\ and so 
of lines drawn to any other point. The line DD \ drawn 
through the foci and terminated by the curve, is called 

What is a plane surface ? What a plane figure? What is an ellipsa? Describe ii 
from figure. 



EXPLANATORY CHAPTER. 



21 



tne major axis of the ellipse. The line PP l , drawn 
throu/^ C, the middle of DD l , or the centre of the fig- 
ure, xs the conjugate axis. 

17. TV Construct an Ellipse. Stick two pins into 
a, pieoe of pap ■ at a short distance from each other, as 
at F and F 1 , and pass over them a loop of thread, place 
a pencil in the loop, and keeping the thread tight, a tri- 
angle will be formed ~ke FMF 1 , the pencil being at M. 
Passing the pencil completely round F and F 1 , its point 
will mark out an ellipse. 2 ur since in making the circuit, 
the length of the loop does not "change, neither the dis- 
tance between F and F 1 , it necessarily follows that the 
su2*» of the distances from the pins to the pencil; viz., 
x X M, FM, &c, is invariable. 

18. Eccentricity. Ellipses differ among themselves. 
±x the foci are near the centre of the ellipse, the ellipse 
approaches the form of a circle ; but if the foci depart 
widely from it the length of the conjugate axis is small 
in proportion to that of the major axis, and the ellipse 
is said to be very eccentric. l 

The distance from the centre to either focus ; viz., FC, 
or F l G, is termed the eccentricity of the ellipse. In 



FIG. 10. 



FIG 9 




bigs. 9 and 10, two ellipses are exhibited which differ 
greatly in their eccentricity ; one being almost a circle, 
and the other very oval. 

1. Eccentric, from ex out of , and centrum centre, (Latin) out of tht 
centre. 

Construct an ellipse 1 What is meant by the term eceentricity 1 



22 ASTRONOMY. 

19. A Sphere. A sphere is a solid, bounded by a 
curved surface, every point of which is equally distant 
from a point within, called the centre ; every line pass- 
ing through, this centre, and limited by the surface, is a 
diameter. The half of this line is . a radius of the 




A SPHERE WITH ITS SECTIONS. 

sphere. Thus in Fig. 11, representing a sphere, the 
points D, 0, L, A, E, H, N, &c, are all equally distant 
from the centre C. DE and AB, are diameters, and 
CP, CL, CA, CB, &c, are each a radius. 

If a plane passes through a sphere, any section it 
makes with the sphere is a circle. A great circle passes 
through the centre of the sphere, all other circles are 
small "circles. Thus in the figure, AFB is a great circle } 
and LHN and OP small circles. 

20. Poles of a Circle of a Sphere. The poles of 
a circle of a sphere are points on the surface of a sphere^ 
equally distant from every point in the circumference of that 
circle. Thus, D is the pole of the circle LHN, because 
the curved lines DH, DN, and DOL, and all others 

What is a sphere? Describe it from the figure with its lines rind sections * What ar« 
*»e poles of a circle of a sphere 1 Explain from figure. 



EXPLANATORY CHAPTER 23 

drawn to the circumference LHN, ai*e equal to one 
another. For the same reason D is the pole of the cir- 
cles OP and AB. It will also be seen that the point E 
is situated like D, with respect to these circles, since the 
curved lines EBN and EAL are equal, as likewise ELO 
and ENP. Each circle of a sphere has therefore two 
poles. 

In a great circle the poles are each ninety degrees dis- 
tant from the circumference of the circle, thus in the 
great circle AB, the poles E and D are each ninety de- 
grees from its circumference AFB. 



24 THE EAETH VIEWED ASTRONOMICALLY. 



PART FIRST. 

IRK EARTH IN ITS RELATION TO OTHER HEAVENLY BOD1II, 



CHAPTER I. 

ITS FORM, SIZE, ROTATION, AND DENSITY. 

*i. Its Form. The earth appears to our view to be 
nothing more than a vast broken plain, rising into 
mountains, sinking into vallies, and spreading out into 
lakes, seas, and oceans ; but a careful investigation re- 




moves this erroneous impression and proves, First that 
the general surface of the earth is curved ; /Secondly, that 
the mass itself is nearly spherical in form ; Thirdly, that 
it rests upon nothing. 

22. These facts are established by several independent 
proofs. In the first place when a vessel sails from the 
shore the spectators upon the strand, as they watch her 
lessening in the distance, at length perceive the hull 
gradually sinking below the line of the horizon 1 ; next 

1. Horizon, a boundary. It here means the line that apparently divides 

What does Part First treat of? What does Chapter First treat of? What appear- 
ance does the earth present ? What facts have b&?n proved by careful investigation 1 
State the several proofs of tbeso facts ? 



ITS FORM. 25 

the lower sails disappear, and the last objects that are 
seen are the tops of the masts, on a level with the dis- 
tant waters ; and this is the case in whatever direction 
the vessel sails. Secondly, navigators have repeatedly 
sailed around the earth, by advancing constantly in the 
same direction; arriving at length at the port from 
whence they departed. 

Thirdly, On the ocean the horizon appears to be the 
circumference of a circle, and by the aid of geometry it 
can be proved to be really so. Indeed, any where on 
land or at sea the visible portion of the earth's surface 
is circular, and the higher we ascend above the level of 
the ocean, the larger does this circle become. At the 
top of Mount ^Etna, 10,872 feet high, one-four thou- 
sandth (4/0 o-th) part of the surface of the earth is 
beheld, while from a balloon elevated 25,000 feet above 
the ocean, the sixteen hundredth part (xeV o tn ) nas ^ een 
seen. The fact that the visible portion of tne earth's 
surface is circular, at what place soever an observation 
is made, can be accounted for only upon the supposition 
that the earth is spherical ; and this point may be illus- 
trated in the following manner. If we take an orange 
to represent the earth, and cut off a smooth slice from 
any side of it, the outer surface of the slice may be re- 
garded as the visible portion of the earth's surface seen 
by a spectator. A single glance will show that the 
bounding line of this surface is the circumference of a 
circle. If instead of a globular bod^, like an orange, we 
take a lemon, the slices or sections will be circular, only 
when they are cut off perpendicular to a line joining the 
two ends. If a slice is cut off from the side, it will be 
oval in shape. Indeed, what body soever is taken, the 
sections made on any side of it, will not be circular 
except that body is a sphere. 

Fourthly, When the sun, earth, and moon are so 
situated that they are all in the same straight line, the 
earth being between the others, it casts a shadow upon 
the moon. This shadow is seen to be circular in form, 
thus proving that the earth is round. 

the surface of the earth from the sky and limits our view Its full m eaning 
is explained in Art. 36, 37, and 38 



26 THE EARTH VIEWED ASTRONOMICALLY. 

Fifthly, Since the sun, and the nearest heavenly bodiea 
are seen to be round, we naturally infer that the earth 
does not constitute an exception, but has also a similar 
*brm. 

Sixthly, From observations and actual measurements, 
mathematicians are able to compute the distances of 
places on the earth's surface from its centre; in numer- 
ous places widely differing in latitude and longitude 
these distances have been computed, and are found to be 
in all instances nearly equal. This fact proves the 
spherical shape of the earth, since a sphere alone of all 
solid bodies possesses the property, that the distance 
from the centre to any point on its surface is every- 
where the same. 

In view of all these facts we conclude that the earth 
is a body having a curved surface, that it is nearly spherical 
in shape, and rests upon nothing. 

23. We say nearly spherical, for according to the most 
accurate observations and refined calculations of astrono- 
mers, the earth swells out at the equator, the diameter 
which passes through it from pole to pole, l being 
about one three hundredth part (3 \ ¥ th) shorter than any 
diameter that passes through the equator. To such a 
solid geometricians have given the name of oblate 
spheroid. 

24. Size of the Earth. The diameter of the earth 
can be approximately determined in the following man- 
ner. Regarding it as a sphere, let BDC, in Fig. 13, 
represent a section of the earth through its centre, and 
AB, the height of a mountain above the sea level ; while 
AD is an imaginary line drawn from the top of the 
mountain touching the earth at D, on the distant 
horizon. 

Now a mathematician can easily obtain by the aid of 

1. The polar diameter of the earth is the imaginary line or axis about 
which the earth rotates, like a wheel on an axle. Its extremities are the 
poles of the earth. A diameter drawn at right angles, to the polar diame- 
ter, and passing through the centre of the earth is an equatorial diameter. 
(See Fig. 12.) 

Is the earth exactly spherical 1 How much shorter than the equatorial diameter is the 
polar? What is the geometrical name of a solid body shaped like the earth % Explain 
the first method by which the diameter of the earth can be nearly determined ? 



SIZE OF THE EARTH. 27 

FIG. 13. 




A SECTION OF THE EARTH. 



trigonometry l both the height of the mountain AB, and 
the length of the line AD, and geometry then informs us 
that there are such relations existing between the lines 
AD, AC, and AB, as can be expressed by the following 
proportion; viz., AB: AD: : AD: AC. The length of 
the line AC, is then ascertained by the rule of three. 
AC, therefore equals 

AD x AD 
AB. 
Subtracting now the height of the mountain AB, from 
the length of AC, and there remains the length of BC, 
the diameter of the earth. Thus if a peak of the Andes, 
4 miles high, is just visible on the Pacific Ocean at 
the distance of 178i miles, the diameter of the earth 
and the height of the peak (AC) would together equal 

178i x 178j 
4 
or 7,943.26 miles ; diminishing this quantity by four we 
have 7,989.26 miles for the diameter of the earth. Pro- 
ceeding then by the common rule for finding the cir- 
cumference of a circle from the diameter, we multiply 
7,939.26 by the number 3.14159 which gives a product 
of 24,942 miles for the circumference of the earth 2 . 

1 . Trigonometry " that science which teaches how to determine the 
several parts of a triangle from having certain parts given." 

2. Another solution is here given for those versed in algebra and ge- 
ometry, E being the centre of the circle, let x = the radius BE, or ED, 

2 
then, (x + 4) a = x 2 + 178,25.-. x»+8x-M6 = x a + 3,1773.0625 .• 



28 THE EARTH VIEWED ASTRONOMICALLY. 

25. There exists another method for determining the 
size of the earth, which was employed by Eratosthenes, 
a celebrated astronomer, who flourished at Alexandria 
in Egypt, about 200 years before Christ. The mode of 
operation may be explained as follows : If it were pos 
sible for a person to start, for instance, from Washing- 
ton, in a north or south direction, measuring round the 
earth until he came to Washington again, he would have 
passed over three hundred and sixty degrees of latitude. 
Now on the supposition that the earth is a sphere, it is 
clear that any number of degrees of latitude, as five for 
example, bears the same relation to the length of the 
same number of degrees in miles, as three hundred and 
sixty degrees of latitude to the entire circumference of 
the earth, measured in miles ; since five is the same part 
of three hundred and sixty, as the length of five degrees 
in miles, is of the circumference of the earth in miles. 

26. It was in this manner that Eratosthenes proceeded. 
He found that Alexandria in Egypt, was 500 miles 
north of Syene, a town on the frontiers of Nubia, and 
that the difference in latitude between the two places was 
7} degrees. From tliese measurements he was enabled 
to make the following proportion, 7} degrees : 500 miles 
: : 360 degrees : the circumference of the earth in miles. 

The fourth term therefore equals 
360 x 500 

n 

or 25,000 which expresses the circumference of the 
earth in miles. 25,000 divided by 3.14159 gives the 
diameter. In round numbers, we may therefore con- 
sider the diameter of the earth to be 8,000 miles in ex- 
tent and the circumference 25,000. But astronomers 
have not remained contented with these rough approxi- 
mations towards the truth, since all accurate knowledge 
of the distances, magnitudes, and motions of the other 
heavenly bodies, depends upon our knowing the exact 
dimensions of the earth. The latest and most elaborate 

8 x = 31757.0625T!T^nS69SPwS 2 = 7939.26 the 

diameter of the earth. 

Explain th* method employed by Eratnsthenetf. What is the length of the diameter of 
me earth in miles, in round numbers 1 What that of the circumference ? 



ROTATION OF THE EARTH. 29 

researches demonstrate that the length of the polar di- 
ameter of the earth, is 7,899.170 miles, and that of the 
equatorial diameter 7,925.648. The distance from the 
general surface of the earth to the centre, being at the 
equator 13.239 miles greater than at the poles. 

27. Rotation of the Earth. To every one en- 
dowed with vision, it is one of the most familiar 3ights 
in nature to behold the sun ascend the eastern sky, at- 
tain its noontide splendor, and at length set beneath the 
western horizon. And when night approaches the starry- 
host appear moving in the same order ; their bright ranks' 
rising successively above the eastern horizon, and pass- 
ing over in ceaseless march to the west. This motion 
of the celestial bodies can be explained in two ways, 
either by supposing that the earth is at rest, and all the 
luminaries of the sky actually revolve about it, or that 
their motion is only apparent 1 , the earth itself really 
rotating while the celestial orbs remain immoveable. 

The first theory was received as the truth for ages, 
until the discoveries of scientific men at length showed 
its falsity, and established by undeniable proofs, the 
fact of the rotation of the earth on its axis. Some of 
these proofs we shall now state. 

28. First proof. The form under which atoms of mat- 
ter unite in obedience to their mutual attraction, and un- 
influenced by any other force, is that of a sphere. We 
behold this exemplified in the case of quicksilver spilled 
upon a floor, the small portions of which are seen as- 
suming a globular shape, the form being more perfect as 
the portion is smaller. Moreover if alcohol and water 
are mingled together, in such proportions as to have the 
same 2 specific gravity as olive oil, upon dropping a little 

1. When a person sails from the shore with a steady wind, the shore ap- 
parently moves backward, while the ship seems to be stationary though 
the observer knows all the while that the true state of the case is exacSy 
the reverse. 

2. Two substances are of the same specific gravity, when being equal in 
size they are also equal in weight. 

What are the lengths of the equatorial and polar diameter according to the best and 
latest computations ? How much farther is the surface of the earth from the centre at the 
equator than at the po»es 1 In how many ways can the motions of the celestial bodies 
be explained? What are those ways 1 Which one for ages was received as true ? Hat 
it been proved false. 



«Hi/ HfK kaktu vkkwhi* astronomically, 

of the latter into the mixed fluid, the drops of oil uninflu- 
enced by the gravitation of the earth, take the shape of 
spheres as long as they are at rest. But if now a slender 
wire is passed through the centre of one of these oil- 
globes, and it is made to revolve by turning the wire 
rapidly round, it flattens about those points where the 
wire passes through, which represent the poles of the 
oil-globe, while it swells out at the middle or equatorial 
parts, assuming the form of a spheroid, in consequence 
of the centrifugal 1 force increasing from the poles to the 
equator. 

29. In like manner if the earth at the beginning con- 
sisted of yielding materials, as many able geologists 
suppose, it must have assumed the shape of a sphere by 
virtue of the mutual attraction of its particles, and re- 
tained that shape forever, provided it did not rotate on 
an axis ; but if it did thus rotate, it must have taken 
the form of a spheroid, the amount of the excess of the 
equatorial diameter over that of the polar, depending 
upon the rapidity of the rotation. 

30. Taking as the ground- work of his computation 
the known dimensions of the earth, and assuming as 
a fact' its revolution in twenty -four hours; Sir Isaac 
Newton calculated what form the earth must of neces- 
sity take. He found it would be a spheroid, and that 
the equatorial diameter, would exceed the polar diameter 
by a certain length, which is almost exactly equal to the 
difference which has since, by the actual measurement 
of the earth, been shown to exist between them, viz., 
twenty -six miles and nine-tenths of a mile. 

The result of the computation being thus proved true, 
the assumed point upon which this result is founded, 

1. Centrifugal force, is that which tends to make a revolving body 
depart from the centre of motion. Water flying from the circumference 
©f a revolving grindstone, is an example. When bodies revolve in differ- 
ent circles, in the same time the centrifugal forces are directly proportioned 
either to the radii or circumference of the circles. The centrifugal force, 
reckoning from the poles of the earth to the equator, will therefore increase 
in the ratio of the length of the parallels of latitude. 

State the first proof that the earth rotates on its axis 7 What was the result of Sh 
Isaac Newton's computation ' 



DEVIATION OF FALLING BODIES, &C. 



31 



FIG. J4. 



must be also true. The rotation of the earth is, there- 
fore, no longer a supposition, but a fact. 

31. Second Proof. — Deviation of Falling Bodies 
from A vertical line. If the earth has indeed a rota- 
tion on its axis, all the particles that compose it, and all 
the bodies upon its surface, have a greater centrifugal 
force in proportion as they are more distant from the 
axis of rotation. Thus, a particle of dust upon the top 
of a carriage wheel in rapid motion, flies off in advance 
with greater velocity than if it had been situated nearei 
the axle ; and in like manner, if the earth is actually ro- 
tating from west to east, a ball upon the top of a lofty 
tower, will move with greater speed towards the east 
than when placed at the bottom, because in the first posi- 
tion it is farther removed from the axis of rotation, than 
in the second. 

32. With this principle in view, a 
simple experiment reveals the fact of 
the rotation of the earth. If the earth 
were at rest, a bullet dropped from the 
top of a high tower, would descend in 
a line parallel to the perpendicular 
height of the tower ; the point where 
it struck the ground, and the point 
whence it started, being at the same 
distance from the middle of the tower. 
But upon making the experiment it is 
found that when the bullet is dropped 
on the east side of the tower, it reaches 
the earth at a point farther east from 
the centre of the tower, than the place 
of starting. Now this circumstance 

can only be explained, on the supposition that the earth 
rotates from west to east, and imparting the greatest cen- 
trifugal force to the bullet, when at the top of the towei, 
and the least at the bottom, it necessarily gives it an 
easterly motion beyond the perpendicular. Thua, in 
Fig. 14, CC l represents the perpendicular height of a 
tower, BB 1 the same, and BD tfte pach of a bullet 
dropped from the top of the tower on ike eastern side. 




B'D 



2* 



Give the second proof 



82 THE EARTH VIEWED ASTRONOMICALLY. 

The distance from the place of starting to the centre of 
the tower ; viz., CB, is less than the distance of the place 
where the bnllet strikes the earth from the centre of the 
tower, viz., G l D.( l ) 

33. Third Proof. — Variation in the Weight of 
Bodies. It has been discovered by philosophers, from 
experiments with the pendulum, that a body weighing 
194 pounds at the equator of the earth, would weigh 195 
pounds at the poles, or in other words, would gain T £ T th 
part of its weight by such a removal. It might at first 
be supposed, that this circumstance is owing to the fact, 
that a body at the poles is thirteen miles nearer the 
centre of the earth than at the equator, and thus beiog 
more powerfully attracted would of course weigh more. 
But the increase of weight arising from this cause is 
only Triirth part of the original weight, and the differ- 
ence between xi?th and sl<yth, viz, a iyth, remains un- 
accounted for on the supposition that the earth is at 
rest. When, however, we regard the earth as rotating 
on its axis once in twenty-four hours, the difficulty 
vanishes, for at the equator bodies are acted upon by 
two forces ; 1st, the force of gravity, which draws 
them towards the centre of the earth, and is a mea- 
sure of their weight ; and 2d, the centrifugal force of 
the earth, which tends to make them fly away from 
the centre, and diminishes their weight. At the poles 
this centrifugal force is nothing. Now at the equator, 
the centrifugal force is directly opposed to the force 
of gravity, and diminishes its effect ; thus lessening 
the weight of bodies, according to the profound inves- 
tigations of eminent mathematicians, ?|$th part. The 
fact of the variation in the weight of bodies in differ- 
ent parts of the world can thus be fully accounted for, 
but if the rotation of the earth is denied, it remains 
inexplicable. A fourth proof of the earth's rotation 
is afforded by the pendulum. 2 

34. In view of these and other equally important 

1 . An experiment of this kind was performed by Benzenberg, a Ger- 
man, in 1802, in Michael's Tower, at Hamburg, 30 balls being dropped 
from the height of 235 feet. The deviation from the perpendicular was 
one-third of an inch. See Appendix. I 

Give the third proof. What inference is made in view of the facts adduced ? 



SENSIBLE HORIZON. 33 

facts, which will appear in the course of our investi- 
gations, we infer that the earth rotates as though revolv- 
ing on u diameter, at right angles to the plane of the 
equator. The period of rotation, as we shall hereafter 
see, is divided into twenty-four equal parts, called 
hours. 

35. Density. The density of the earth is ascer- 
tained by comparing the amount of attraction which 
it exerts upon any object with that which a body of 
known mass exerts upon the same object. From nu- 
merous experiments conducted in ' accordance with 
this principle, it appears that the earth, on an average, 
is about five and a half times (5.46) heavier than 
water. 1 



CHAPTER II 

THE HOKIZON. 



36. Horizon is an astronomical term derived trom 
the Greek word orizon signifying boundary, and of these 
boundaries there are two. 

Sensible Horizon. The first is the sensible or visi- 
ble horizon, of which we have already spoken. It is 
the line apparently separating the earth and sky, and 
which a spectator upon the expanse of ocean, or on a 
vast unbroken plain, perceives to be a circle. 

The plane of the visible horizon is regarded as touch- 
ing the earth at the point where the spectator stands, 
though strictly speaking this is not the case, since on 
account of the depression of the visible horizon the 
point where the spectator stands is a little above its 
plane. This is evident by referring to Fig. 15, where the 
circle B represents a section of the globe, S the place of 
the spectator, and the circular line YH a part of his 
visible horizon. Now it is evident at a glance, that 
owing to the curvature of the earth the plane of the visi- 
ble horizon, which takes the direction V l VHH l , is neces- 

See Appendix. II, 

How is the period of rotation divided ? What is said respecting the density of the 
earth? What does Chapter Second treat of? What is the meaning of the term 
horizon ? Giye the Boning of the term sensible horizon, and explain from figure. 



34 THE EARTH VIEWED ASTRONOMICALLY. 

sarily below the parallel plane that touches the earth at 
S, the place of the spectator, and takes the direction of 
ASA 1 . Nevertheless the difference in distance between 

FIG. 15. 




HORIZON EXPLAINED. 



the two planes is usually so small that they are generally 
regarded as coinciding ; the plane of the horizon being 
supposed to pass through S. 

37. Rational Horizon. The second or rational hor- 
izon is a vast imaginary circle whose plane passes 
through the centre of the earth, dividing the earth and 
sky into two hemispheres, and is parallel to the plane of 
the visible horizon. It is also represented in direction 
in Fig. 15, by the line RR\ 

At the earth these planes are nearly 4,000 miles 
asunder, or half the diameter of the globe, but when we 
extend them in imagination as far as the fixed stars, 

Of rational horizon, and explain from figure How far apart are these planes at the 
rartb 1 Wbv will these planes appear to meet at the distance of the fixed stars ? 



PLANE OF THE HORIZON NOT FIXED IN SPACE. 35 

they are there supposed . to meet. l For a spectator at 
such a distance from, the earth, if he could possibly dis- 
cern our globe, would see it as a mere point ; and the 
E lanes of the two horizons would apparently meet, there 
eing no visible distance between them. In the same 
manner, if a person on the earth could really behold the 
planes of the horizons as visible surfaces, actually ex- 
tended in all directions to the fixed stars, he would 
see them coinciding, and intersecting the concave 2 sphere 
of the visible heavens in the same line ; for the space of 
4,000 miles by which they are separated, would at this 
immense distance apparently dwindle also in this case to 
a mere point. For these reasons it is said that the planes 
of the sensible and visible horizons cut the concave sur- 
face of the distant heavens in the same line. 

38. Plane of the Horizon not fixed in Space. 
We have said that the plane of the horizon touches the 
surface of the earth at the point where the spectator 
stands, or in other words, is at right angles at this point 
to a plumb-line 3 passing through this same point. 
Now the direction of the plumb-line varies at every point 
of the earth's surface. Consequently, there are as many 
horizons both sensible and rational as there are such 
points; and the planes of these horizons take all possi- 
ble directions. Thus, in Fig. 15, if S, S l , S 2 , represent 
the stations of different spectators upon the earth's sur- 
face, it is clear that the planes of the horizons of each, 
viz, AA 1 , A 2 A 3 , A 4 A 5 , take different directions. 

1. Strictly speaking two parallel planes or lines extended to any dis- 
tance can never actually meet, they only appear to the eye to meet. 
Thus, to the view of a person standing on a rail-road where the track is 
straight for a considerable length, the parallel rails in the distance seem 
to approach nearer and nearer to each other, according as they are 
more remot : from the spectator, though they are really as far ap:irt in 
one place as in another. If the straight track is very long they will 
appear to meet and come to a point. 

2. If a sphere is hollow the inner surface is termed a concave sphere 
The visible heavens appear to have this form 

3. It a ball of lead is tied to one end of a string, and the other end 
held up so that the ball can swing freely, the direction the string takes 
when the ball is at rest is the direction of the plumb-line. Plumbum 
is the Latin word for lead. 

Is die i»!<tne of the horizon fixed in space? How many b mzons are thei»? Ey 
'^lain from figure. 



86 THE EARTH VIEWED ASTRONOMICALLY. 

39. Zenith and Nadir. The point in the heavens, 
in the direction of the plumb-line, exactly over the head 
of an observer, is the zenith ; and the point in the heavens 
beneath him in the opposite direction is the nadir. ' The 
zenith and nadir are the poles of the rational and sensi- 
ble horizons, since they are points in the concave sphere 
of the heavens, ninety degrees distant in every direc- 
tion from the common line where the planes of both 
these horizons cut this sphere. 

Since the horizon of an observer changes at every 
step, it necessarily follows that his zenith and nadir also 
change. The zenith of the place directly beneath us on 
the opposite side of the earth is our nadir, and its nadir 
our zenith. In Fig. 15, Z is the zenith at S, and N the 
nadir, At S 1 , Z l is the zenith and N 1 the nadir. At 
S 2 , Z 2 is the zenith and N 2 the nadir. 

40. Changing Aspect of the Heavens arising 
from the Eotation of the Earth. Having learned 
the fact of the rotation of the earth, and of the full 
meaning of the term horizon, we will now contemplate 
the aspect of the starry sky, remembering all the while 
that we are not stationary, but standing on the surface 
of a rolling ball. 

41. If, in our latitude, upon a clear evening, we take 
a position upon some commanding eminence, we per- 
ceive the whole of the overarching sky studded with 
multitudes of glittering stars, down to the very line 
which separates the earth from the heavens. Some 
bright cluster may perhaps be seen just hanging above 
the western horizon, while another may arrest our atten- 
tion in the eastern sky. 

Time glides away unheeded as the glories of the 
splendid scene pass in review before us, and when we 
turn our eyes again towards the western group it is no 
longer visible, but has sunk beneath the horizon, while 
the cluster in the east has attained a loftier elevation. 

42. By a longer and closer observation we find that 
all the stars have this common motion from east to west, 
and that they appear to move in circular paths. 

What is meant by zenith and nadir? Having now learned the meaning of the term 
horizon, to what ii our attention next directed 1 In what direction do all the st*«» «ui 



CHANGING ASPECT OF THE HEAVENS, &C. 37 

It is moreover noticed, that the stars in passing over 
from the eastern to the western horizon, describe greater 
or less portions of the circumference of a circle, accord- 
ing to their different positions in the heavens. Thus, 
the farther to the north a star rises, the greater is the 
arc 1 it passes through, and the longer it is visible, till 
at last we observe stars far in the north which never sink 
below the horizon, but revolve about some unseen centre 
situated high up in the northern sky. On the contrary, 
in the southern quarter of the heavens the arcs of circles 
described by the stars are seen to be smaller and smaller 
as our eyes are directed to points more and more remote 
towards the south ; until, at the southern extremity of 
the heavens, the bright luminaries scarcely lift their 
heads above the horizon before they begin again to de- 
scend and withdraw from our view. 

43. Our knowledge of the rotation of the earth ren- 
ders these appearances perfectly intelligible. The stars 
are not really in motion, but only appear to be, for the 
earth in its rotation from west to east is constantly de- 
pressing the eastern part of the horizon and elevating 
the western, so that a star rises in consequence of the 
eastern horizon being carried below it, and sets because 
the western horizon is carried up to it and above it. 

44. This point is illustrated in Fig. 16, where circle 
E represents the earth rotating from west to east, 8 as 
shown by the direction of the arrows. If a person is at 
M, on the surface of the earth, the plane of his horizon 
is in the line HH 1 , and the star S is above his western 
horizon, and the star S 1 below his eastern horizon. But 
when the earth in its rotation brings the person into the 
position M 1 , the plane of his horizon has been so changed 
as to take the direction H 2 H 3 , and the star S has set 

1. Arc, any portion of the circumference of a circle. 

2. The phrase, rt jolving from west to east, is explained in Art. 134. 

pear to move, and in what kind of path 1 Do they all describe, in our own latitude, 
equal portions of the circumference of a circle, while above the horizon, and are they all 
visible for the same length of time 1 What is said respecting the stars situated in the 
northern portion of the heavens, and what of those in the southern 1 How i« the motion 
of the stars explained 1 Are they really in motion 1 How do you explain the rising an»> 
letting of a stai 1 Illustrate from the figure 



58 THE EARTH VIEWED ASTRONOMICALLY. 

FIG. 16. 




west. ■ HnraflB HiMSm Beast 



CHANGING HORIZONS. 



below the western horizon, while the star S 1 has risen 
above the eastern. 

45. Why the Stars appear to describe Circles. 
The apparent circular paths of the stars are the result of 
our own circular motion on the surface of the earth ; for, 
not perceiving ourselves to move, these orbs appear 
to have the kind of motion that really belongs to us. 
This illusion is the same as that which happens when 
two trains of cars coming from opposite directions stop 
side by side in a depot, and a passenger in one looks out 
at the opposite stationary train, the moment his own 
starts ; unconscious of his own motion, the train at his 
side appears to him to move in a contrary direction to 
that in which he himself is actually proceeding. If his 
own train moves in a straight line, the other appears to 
do so likewise ; but if the former moves in a circular 
track, such is the apparent course of the latter. In like 
manner a spectator moving in a circle upon the rolling 
surface of the globe, sees the stars moving in circles in 
a direction contrary to his own, imagining himself all 
the while to be at rest. 

46. Why these Circles Differ m Size. The rea- 

Explain why the stars appear to describe circles, and why these circles apparently diflfc 
in size. 



CHANGING ASPECT <>F THE HEAVENS, &C. ^9 

son why the stars apparently describe circles of differ- 
ent magnitudes is the following. If lines were drawn 
from the centre of the globe to the heavens, in various 
directions from the equator to the poles, they would 
describe, as the earth revolved, circles in the sky ; 
whose angular magnitudes would depend upon the 
several inclinations of these lines to the axis of rota- 
tion. Thus a line at right angles to this axis would 
pass through the equator, and describe the greatest 
circle ; while another, down through a parallel of lati- 
tude fifty degrees from one of the poles, would describe 
a circle in the heavens of fifty degrees radius, and pass 
through the stars in the zeniths of the regions situated 
on this parallel. A line drawn from the centre to 
either pole would evidently coincide with the axis of 
rotation ; it could therefore describe no circle, and 
would be at rest. Now, since the motion of the earth pro- 
duces a contrary apparent motion in the stars, the orbs 
directly above the earth's equator will describe greater 
circles than the stars that pass through the zeniths ot 
regions lying north and south of the equator. And the 
circular paths of the stars will become smallerand smaller 
as they are described nearer the two opposite points in 
the heavens, to which axis of the rotation of the earth 
is directed. These points are termed the north and south 
poles of the heavens, and around them all the luminaries 
of the celestial canopy appear to revolve. They are situ- 
ated directly above the poles of the earth, and any star 
at these points would be stationary. One degree and 
a half distant from the north pole of the heavens a 
bright star is found, which is termed the pole star. 

47. Changing Aspect of the Heavens arising 
from change in Latitude. A person standing on the 
surface of the earth at the equator, has the plane of his 
horizon parallel to the axis of the earth. The poles of 
the heavens are consequently situated in this plane, ana 
his horizon appears to pass through them. All the circles 

What is meant by the north and south poles of the heavens ? Would a star at these 
paints appear to move 1 How far from the north pole of the heavens is the pole star 
•iluated ? Describe the celestial apjwaranees of the equator. 



4:0 THE EARTH VIEWED ASTRONOMICALLY. 

of daily motion 1 are therefore perpendicular to the hor- 
izon. A star which rises in the east passes directly 
overhead and sets in the west, and each orb describing 
half a circle above and half below the horizon is, there- 
fore, visible for twelve hours, and then invisible for an 
equal space of time. Far in the north is seen the pole- 
star, which rises above the horizon one degree and a 
half, slowly revolving in a circle only three degrees in 
diameter in the space of twenty-four hours. 

48. If the observer now advances northerly his hor- 
izon constantly changes in position, being depressed 
below the north pole of the heavens, and elevated above 
the south the same number of degrees and parts of a 
degree that corresponds to his latitude. Thus, if he has 
arrived at ten degrees, north latitude, the northern pole 
is ten degrees above his horizon, and the southern ten 
degrees below it. If, at fifty degrees, thirty minutes, 
north latitude, the north pole is fifty degrees and thirty 
minutes above the horizon, and the southern as much 
below it. And if it were possible for a person to attain 
the distance of ninety degrees, north latitude, and stand 
upon the northern pole of the earth, his horizon would 
be parallel to the equator, the north pole of the heavens 
would be ninety degrees from the horizon, that is, in the 
zenith, and the southern pole of the heavens would 
coincide with his nadir. 

49. This change in the relative positions of the poles 
of the heavens and the horizon produces a correspond 
ing change both in the inclination of the circles of daily 
motion to the horizon, and in the period of visibility 
of different stars. For, all the stars apparently re- 
volve in circles, at right angles to the imaginary line 
joining the poles of the heavens, called the axis of the 
heavens, and as the north pole of the heavens is elevated 
more and more above the horizon, these circles of daily 

1. By the term circles of daily motion, is understood the circles described 
by the heavenly bodies in their apparent daily motion from east to west. 

What changes occur as an observer advances towards the north 1 If he stood upon 
the pole where would the north pole of the heavens be 1 Where the south ? What cor- 
responding changes are produced by the variations in position incident to the poles of the 
baavens and the horizon? What is the axis of the heavens 1 



CIRCLE OF PERPETUAL APPARITION. 41 

motion must cut the horizon more and more obliquely, 
until at the north pole of the earth a person would see 
the stars revolving about him in circles parallel to the 
horizon. 

50. Moreover, when the north pole of the heavens 
rises above the horizon, and the south sinks below it, it is 
only those stars that are situated directly above the earth's 
equator which are visible in a clear sky for twelve hours 
above the horizon, and are absent as long below it ; since 
the centre of their circle of daily motion is alone in the 
plane of the horizon. All the stars to the north of the 
equator have the centres of their circles of daily motion 
more and more elevated above the plane of the horizon 
according as they are situated farther to the north. The 
circumferences of the circles they describe, it is true, be- 
come smaller and smaller, but the arcs described above 
the horizon are proportionally larger ; and consequently 
the time that a star is visible increases up to a certain 
limit from the equator towards the north. 

51. Circle of Perpetual Apparition. There are 
stars which never set ; for when an orb is at a less dis- 
tance from the pole than the horizon is, it is evident 
that such a star will continue to revolve about the poles 
without ever sinking below the horizon. A circle 
around the elevated pole having a radius equal to the 
altitude of the pole above the horizon is called the circle 
of perpetual apparition, because the stars within it never 
set. This circle changes in size with the change of lat- 
itude. In latitude ten degrees its radius is ten degrees ; 
in latitude fifty degrees, fifty degrees ; and at the pole 
it would be ninety degrees, comprehending the entire 
visible heavens, every star above the horizon revolving 
in a circle parallel to it. 

52. Let us now direct our attention to the stars towards 
the south pole, our place of observation being the north- 
ern hemisphere. In this direction the axis of the heavens 
is depressed below the horizon, the south pole of the 

How would the stars appear to revolve to a spectator at the north pole ? What ii 
■aid respecting the times of visibility of stars at the equator and north of the equator? 
Are there stars which never set? What is meant by the circle of perpetual apparition ? 
State what is respecting the extent of the arc described by stars south of the equator, and 
of the extent of their times of visibility. 

4* 



42 THE EARTH VIEWED ASTRONOMICALLY. 

heavens being as far below the horizon as the north pole 
is above it. The centres of the circles of daily motion de- 
scribed by the stars being in this region below the hori- 
zon, the arcs they pass through above the horizon are 
less than semi-circumferences, 1 growing smaller and 
smaller the farther to the south a star is situated. Their 
periods of visibility will decrease in like manner, until we 
arrive at a point in the southern heavens where a star 
j list glimmers for a moment upon the horizon and then 
sets again. 

53. Circle of Perpetual Occultation. The stars 
that are situated at a less distance from the south pole 
of the heavens than the pole is depressed below the hor- 
izon, will never in their daily revolution come into sight. 
A circle around the depressed pole, having a radius 
equal to the distance of this pole below the horizon, is 
called the circle of perpetual occultation, because the stars 
within it never rise to our view. 

54. Like the circle of perpetual apparition, that of 
occultation varies with the variation of latitude, and at 
the same place the magnitude is the same, since one 
pole is elevated the exact amount that the other is de- 
pressed. Thus, in north latitude ten degrees, the south 
pole of the heavens is ten degrees below the horizon, and 
the radius of the circle of perpetual occultation is also 
ten degrees. In north latitude fifty degrees, it is fifty 
degrees, and at north latitude ninety degrees, that is, at 
the north pole of the earth, it comprises the entire half 
of the heavens below the horizon. 

55. We have thus far described the changing aspect 
of the heavens, by supposing a traveler to proceed from 
the equator towards the north.; were he to take the op- 
posite direction and move towards the south, the phe- 
nomena we have described would be exactly the same, 
only reversed in position. Thus, the plane of the hor- 
izon would dip towards the south, the north pole of the 

1. A semi-circumference is half a circumference. 

What is meant by the term circle of perpetual occultation? How does the circle of 

Eerpetual occultation compare in extent with that of perpetual apparition"? What would 
e their extent to an observer at either pole of the earth 1 State what is said respecting 
the phenomena of the heavens when tne observer advances to the south. 



CIRCLE OF PERPETUAL OCOULTATION. 



43 



heavens would be depressed, the southern elevated, and 
the stars would be longer above the horizon south of 
the equator than north of it. To an observer at the 
south pole of the earth, the south pole of the heavens 
would be in ttue zenith, and the circles of daily motior 
would be parallel to the horizon. The circle of perpetual 
apparition would be around the south pole of the heav- 
ens, and that of occnltation about the north, and so on. 
56. These remarks may be still farther impressed 
upon the mind by studying the annexed figure, where 



FIG 17 




fARYING ASPECT OF THE HEAVENS, ARISING FROM CHANGES IN LATITUDE. 



&se outer starred circle represents a section of the con- 
vive sphere of the heavens, C the earth, SP and NP 
its north and south poles, the line SPNP its axis of 



Explain the figure. 



44 THE EARTH VIEWED ASTRONOMICALLY. 

rotation, and EQ its equatorial diameter. S*P l and !N" l P 
are the north and south poles of the heavens, and the 
imaginary line, S^N 1 ? 1 , the axis of the heavens, 
about which the stars apparently revolve. E*Q l is the 
diameter of the celestial equator. 1 1, 1 j 2. 2 ; 3, 3; &c, 
are the diameters of other circles, in the circumferences 
of which the stars appear daily to revolve. If a spec- 
tator is at the equator, at E, his sensible horizon co- 
incides with his rational, S l P l N'P l , at the vast dis- 
tance of the fixed stars ; and the poles of the heavens, 
are consequently upon nis sensible horizon. Thus sit- 
uated, we see that the circles of daily motion are per- 
pendicular to his horizon, and each of the stars that are 
seen at all, apparently describes a semi-circumference 
above and a semi-circumference below the horizon, being 
lor twelve hours visible and for twelve hours invisible. 
This is evident, since the diameters of these circles have 
their centres, as V,/ g, h, &c, in the plane of the horizon. 
If the observer moves to 0, north latitude, forty degrees, 
LM becomes his rational horizon. The north pole of 
the heavens is elevated, and the south depressed forty 
degrees. 2 The radius of the circle of perpetual appari- 
tion, is MR, whose angular breadth is also equal to forty 
degrees, and LV, having the same extent, is the radius 
of the circle of perpetual occultation. The circles of 
daily motion are here oblique to the horizon, LM, and 
the stars north of the equator are consequently above 
the horizon a proportionally longer time than twelve 
hours, as they are nearer the circle of perpetual appari- 
tion. South of the equator they are above the horizon 
for a proportionally shorter space than twelve hours, 
the nearer they approach the circle of perpetual occulta- 
tion. These points are evident when we compare the 
parts of the lines, 1, 1 ; 2, 2 ; 4, 4 ; and 5, 5 ; which are 
above the horizon, LM, with the parts that are below, 

1. The diameter of the eelestial equator is the diameter of the earth's 
equator extended to meet the starry heavens. See Art. 64. 

2. N'CM is an angle of forty degrees, and as the rational horizon of 
the spectator at O coincides with his sensible horizon at the distance of the 
fixed stars, the angle of elevation of the pole, N l P*, at his station, O, on 
»he surface, will also be forty degrees. 



DETERMINING THE PLACES OF HEAVENLY BODIES. 45 

viz., 55, 55; 2c?, d% &c. At the north pole, NP, the 
horizon takes the direction of the line E'Q 1 , the north 
pole of the heavens, NT 1 , is in his zenith, and all the 
stars in the hemisphere, E'N'P^ 1 , revolve in circles 
parallel to the horizon: E ! C is at once the radius of the 
circle of perpetual apparition and occultation, since all 
the stars above the horizon never set, and those below 
it never rise above it. If the observer moves toward 
the south pole of the earth, it is clearly seen that these 
appearances are exactly reversed. 

57. Latitude of any Place equal to the Eleva- 
tion of the Pole of the Heavens. From what has 
been just stated, it is evident that the latitude of any 
place is equal to the altitude of the pole of the heavens 
above the horizon. For we have seen that at the equa- 
tor, where the latitude is nothing, the elevation of the 
pole is nothing ; at latitude forty degrees the elevation 
of the pole is forty degrees, and at the poles of the earth, 
or latitude ninety degrees, the pole of the heavens is 
ninety degrees from the horizon, and is in the zenith. 
And the same is true for every latitude, either north or 
south of the equator. 



CHAPTER III. 

ON THE MODE OP DETERMINING THE PLACE OP A HEAYENLT BODY. 

58. The first object of the geographer in describing 
the earth with its kingdoms, cities, mountains, oceans, 
seas, islands, &c, is to determine their exact position on 
the surface of the globe. This he obtains in the case 
of a city, for instance, by finding first, how many degrees, 
minutes, and seconds, it is situated east or west from a 
great circle, called a meridian, 1 passing through the poles 
of the earth and some assumed point on its surface, as a 

1. See Art. 63 for the meaning of the term meridian. 

What is the latitude of any place equal to? What is the subject of Chapter Hit 
What is the first object of the geographer ? In what manner does he determine the posi 
\ion of a city 1 Give an instance. 



46 THE EAKTH VIEWED ASTRONOMICALLY. 

celebrated observatory ; and secondly, its distance in de- 
grees, minutes, and seconds, north or south of the great 
circle called the equator, passing through the centre of 
the earth at right angles to its axis of rotation. Thus, 
for instance, the position of New York City Hall is fixed 
by finding first, that it is situated seventy-four degrees, 
and three seconds (74° 00' 03") west of the meridian 
passing through Greenwich Observatory. This is its 
longitude. Next, that it is distant north of the equator 
forty degrees, forty-two minutes, and forty-three seconds 
(40° 42' 43"). This is its latitude. These two meas- 
urements are sufficient to mark with precision its situa- 
tion upon the globe, for no other spot on its surface 
can have this latitude and longitude. 

59. In a similar way the astronomer determines the 
position of stars in the concave sphere of the heavens, 
by measuring their angular distances from the planes 
of two great circles, at right angles to each other. But 
in order to understand intelligibly the method pursued, 
we must first give our attention to the manner in which 
both the globe and the sky have been intersected by im- 
aginary lines and circles, and to the relations existing be- 
tween them ; bearing constantly in mind that these lines 
and circles are all pure fictions, not one of them really ex- 
isting in nature, but that they have been invented by 
astronomers and geographers simply for the purpose of 
arriving at certain results. Some of these we have al- 
ready described, but shall refer to a few of them again, 
in this connection, since it is highly important that the 
scholar should always have in his mind a clear idea 
respecting these imaginary circles and lines. 

60. Celestial Sphere, Poles, Axes, and Meridi- 
ans. The celestial sphere is the concave sphere of the 
heavens, in which the stars appear to be set. The poles 
of the earth are the extremities of that imaginary line 
upon which it revolves ; the latter is called the axis. If 
any plane passes through the poles and the axis in any di- 

How does the astronomer determine the position of a star ? What is said respecting 
the circles and lines employed by astronomers for this purpose ? What is meant by thi 
celestial sphere 1 The poles of the earth 1 Its axis 1 Terrestrial meridians. Explaii 
*rom figure 



CELESTIAL SPHERE, POLES, AXES, &C. 47 

recti on, its intersection with the surface of the earth is a 
circle, and is called a terrestrial meridian. Thus, in Fig. 
18, which represents the earth and the celestial sphere, 

FIG. 18 




THE EARTH AND THE CELESTIAL SPHERE. 

the line NS is the axis of the earth. 1ST, the north pole, 
S, the south pole, and NES, N1S, N2S, N3S, are ter- 
restrial meridians. 

61. The axis of the earth, extended in imagination 

What is meant by the axis of the celestial sphere 1 The poles of the heavens 1 



48 THE EARTH VIEWED ASTRONOMICALLY. 

each way until it meets the starry sky, becomes the axis 
of the heavens, or celestial sphere, around which all the 
stars appear to revolve. The extremities of this axis are 
the poles of the heavens. Thus, in the figure, where the 
outer starred circle represents a section of the celestial 
sphere, the line N*S l is the axis of the celestial sphere, 
and N 1 and S 1 its north and south poles. The axis of 
the earth is that part of the axis of the heavens, which 
is intercepted between two opposite points on the earth's 
surface, and these two intercepting points are the poles 
of the earth. 

62. If any plane passes through the poles and axis 
of the heavens in any direction, its intersection with 
the imaginary surface of the celestial sphere is a celestial 
meridian. A terrestrial and celestial meridian are, there- 
fore, formed by one and the same plane ; the first occur- 
ring when the plane is intersected by the surface of the 
earth, the second when it is cut bv the concave sphere 
of the heavens. Thus, INPE'S 1 , N l lS»; N 1 2S 1 ,andN 1 3S l , 
are celestial meridians; and NES, N1S, N2S, and N3S, 
their corresponding terrestrial meridians. 

63. The plane of the meridian at any place is perpen- 
dicular to its horizon, and consequently passes through 
its zenith and nadir, dividing the visible heavens into 
two equal parts towards: the east and west. For this 
reason this circle is called the meridian circle, because 
when the sun, in his apparent diurnal revolution, comes 
to the meridian of any place, it is there noon, or mid- 
day ; the Latin word for mid-day being meridies. 

64. Equators. If we suppose a plane passing 
through the centre of the earth, perpendicular to the axis 
of rotation, its intersection with the surface of the earth 
forms a circle called the equator, or terrestrial equator, 
and if this plane is extended in imagination to the fixed 
stars, its intersection with the celestial sphere is also a 
circle, called the celestial equator, or equinoctuu. Thus, 
in Fig. 18, EQ is the equator, and E'Q 1 the celestial 

What is meant by celestial meridians? Explain from figure. What aie the rela- 
tive positions of the plane of the meridian of any place and the plane of its horizon? 
What is the meaning of the term meridian? What is the terrestrial equator? VVIml 
<4>e celestial ? 



VERTICAL CIRCLES. 49 

equator. They appear as straight lines in the figure, 
because we see them in the direction of their planes. 

65. Vertical Circles. Vertical circles are those 
which are imagined to be formed by planes passing 
through the zenith, perpendicular to the horizon, and 
intersecting the celestial sphere. The vertical circle 
passing through the east and west points of the horizon 
is termed the prime vertical, while that which intersects 
the north and south points becomes a meridian. Thus, 
in Fig. 19, where A represents the earth, SZWMN the 
celestial sphere, Z the zenith, and the plane SWJtfE the 
horizon — PZHM is a vertical circle, WZEM the prima 
vertical, and SZNM a meridian. 

FIG. 19 




AZIMUTH AND ALTITUDE OF A STAR. 



66. The Position of a Star — how determined. 
The place of a star in the sky may be determined in 
three ways. First, by referring it to the planes of a 
celestial meridian and of the horizon. Secondly, by 
noting its distance from the planes of a given meridian 

What are vertical circles ? What the prime vertical ? Is a meridian a vertical circle 1 
Expluin from figure. In how many way* is the position of a star fixed? Describe them 



50 THE EARTH VIEWED ASTRONOMICALLY. 

and the celestial equator. Thirdly, by referring it to the 
planes of a given great circle, and the ecliptic- ' 

67. Azimuth, Amplitude, Altitude, and Zenith- 
distance. Proceeding according to the first method, 
we should ascertain the situation of a star in the follow- 
ing way. Suppose the star is the beautiful luminary, 
Air ha Lyras, and that we observe it in the east. Hav- 
ing previously found the plane of the meridian, by 
methods hereafter to be explained, we should now im- 
agine a vertical circle to pass through our zenith and 
the star, cutting the horizon at right angles. Then, with 
the proper instrument, we should measure on the horizon 
the angle which the vertical plane makes with the me- 
ridian. This angle is called the azimuth of the star, 
and is reckoned from north to south when a star is north 
of the prime vertical, and from south to north when 
south of the prime vertical. The difference between 
the azimuth and ninety degrees is the distance of a star 
from the prime vertical, and is called the amplitude. 

68. The next step is to ascertain the angular elevation 
of the star above the horizon, measured on the vertical 
circle passing through the orb. This angular distance is 
called the altitude of the star, and the difference between 
its altitude and ninety degrees is its zenith distance. By 
having the azimuth and altitude of a star we thus fix 
its position in the sky, at any given time and place. 

69. The subject is illustrated by Fig. 19. Let A rep- 
resent a place on the earth ; Z, the zenith of the place 
where an observer is stationed ; NEHRW, the circle of 
the horizon; 2 SZNM, the meridian circle; ZWEM, the 
prime vertical ; B, a star, and ZBHMP, a vertical circle 
passing though the zenith and the star, B: all these 
circles being circles of the celestial sphere. Then the 
angle NAH, is the azimuth; EAH, the amplitude; 
BAH, the altitude ; and ZAB, the zenith distance of the 

1. For the meaning of the word ecliptic, see Art. 73. 

2. It will be remembered that the planes of the sensible and rational 
horizons virtually meet at the distance of the fixed stars. 

Show how we are to proceed according to the first method. What is meant by the 
terms azimuth, amplitude, altitude, and zenith distance Bhow from the figure how them 
measurements of a star are taken 






DECLINATION AND RIGHT ASCENSION. 51 

star, B. Had the star been situated at P, its amplitude 
and azimuth would have been reckoned from W, to- 
wards S, the former being the angle WAR, the latter SAR. 

70. This method of determining the position of a 
heavenly body is, however, not sufficient for all astro- 
nomical purposes, since, inasmuch as every place on the 
globe has a different horizon, the azimuth, amplitude, 
altitude, and zenith distance of the same star, taken at 
any two places at the same absolute point of time, will 
not be alike. Astronomers have, therefore, devised a 
method of fixing the place of a star in the heavens, by 
measuring its distance from two celestial circles, un- 
changeable in position, whatever point the observer oc- 
cupies upon the surface of the earth. These two circles 
are the celestial equator, and that meridian which passes 
through the centre of the sun in the spring, at the 
moment this centre is upon the celestial equator. This 
point of the celestial equator has received the appellation 
of the vernal equinox. l 

71. Declination and Right Ascension. The an- 
gular distance of a star, measured from the celestial 
equator, on a meridian passing through the star, is called 
its declination, and is termed north or south declination, 
according as the star is situated north or south of the 
equator. Bight ascension is the distance of a star meas- 
ured on the celestial equator in an easterly direction from 
the meridian passing through the vernal equinox. Right 
ascension may be reckoned either by angular measure- 
ment, 8 viz., degrees, minutes, and seconds, or by time, 

1. Ver, the Latin word for spring; equinox, a word formed from two 
Latin words, aquus, equal, and nox, night. The vernal equinox is so 
called because when the sun appears at this point in the heavens, the nights, 
and consequently the days, are equal in length in every part of the world. 

2. The following figure will enable the scholar to understand how angu- 
lar measurements are taken. Let OCD be a portion of a brass circle, the 
arc of which, viz., OD, is divided into degrees and minutes. To the cf ntre, 
C, a telescope, PL, is attached, movable on a pivot at C. Now, if the brass 
arc is held vertically, and the edge, CD, horizontally, and the observer, 

Why is not the position of a star accurately fixed for all astronomical purposes when 
its azimuth and altitude are determined 1 What other mode of measurement has been da- 
vised by astronomers 1 What is understood by the term vernal equinox ? What is decli 
ination ? What is right ascension ? How 19 it reekoned 1 Explain from note 2 how 
angulos measurements are taken. 



52 THE EARTH VIEWED ASTRONOMICALLY. 

viz., hours, minutes, and seconds. For, since all the fixed 
stars in the heavens apparently revolve about the earth 
once every twenty -four hours, any star completes three 
hundred and sixty degrees of angular motion in that 
time ; consequently it seems to move fifteen degrees 
every hour, fifteen minutes every minute of time, and 
fifteen seconds every second of time. So that a star 
which is situated on a meridian fifteen degrees east of 
the meridian passing through the vernal equinox, is said 
to have a right ascension of fifteen degrees, or of one 
hour; inasmuch as one hour elapses between the pas- 
sage of the vernal equinox, and that of the star across 
the meridian of the place of the observer. 

72. The subject is illustrated by Fig. 20, where P re- 
presents the north pole of the heavens, P°i° a celestial 
meridian passing through the vernal equinox, QAQ 1 the 
celestial equator, S the place of a star, PSA a part of a 
celestial meridian passing through the star, and C the 
centre of the celestial sphere ; or what is the same in 
effect the place of the spectator. 

Now the declination of the star is the arc SA, since 
this arc measures the angular distance of the star from 
the equator QAQ 1 . PSA, is one quarter of a meridian 

with his eye at P, then views a star in the direction PCLS, the angle meas- 
ured on the are DO, from D, viz., DCL, or HCS, will be the altitude of the 
star, S, above the horizon, H. In the figure it is fifteen degrees. If the 
brass arc is held horizontally, and the edge, CD, is in a line with the me- 
ridian, the angle SCH will be the azimuth of the star. 




1. The character °f is called Aries and is that point in the celestial 
equator which is termed the vernal equinox. P^j is read thus, P, 
Aries. 

Show from figure what is the declination and right ascension of the star at S 



LATITUDE AND LONGITUDE. 



bo 



passing through. S, and contains ninety degrees, and if 
AS contain forty degrees, the declination of the star is 
forty degrees north. The right ascension of the star is TA, 



fig. 20 




DECLINATION, RIGHT ASCENSION, LATITUDE, LONGITUDE. 

and it this arc contains fifteen degrees the star at S has 
fifteen degrees of right ascension or one hour. 

73. Ecliptic. The imaginary line that the earth de- 
scribes in her annual progress around the sun is termed 
her orbit, and its position in regard to the celestial 
equator is ascertained by tracing the apparent path of 
the sun through the heavens, from day to day through- 
out the entire year. It differs somewhat from the form 
of a circle being an ellipse, and its plane passes through 
the centre of the earth and sun, having an inclination 
to that of the celestial equator of about 23° 27'. Its 
intersection with the celestial sphere is called the eclip- 
tic 1 ; and constitutes what may be regarded as a great 
circle of the heavens. 

74. Latitude and Longitude. In addition to the 
two preceding methods of determining the position of 
the stars, a third has been adopted by referring them to 

1. So called because eclipses happen in or near its plane. 



What is meant by the earth's orbit. Is it a circle ? What is the inclination of iti 
plane to that of the celestial equator? What is the ecliptic'? What is understood b 
the Latitude of a star ? What by its Longitude. Explain from figure. 



54 THE EARTH VIEWED ASTRONOMICALLY. 

the ecliptic, and to a great circle passing through the 
vernal equinox. Thus, the angular distance of a star 
from the ecliptic measured on a great circle passing 
through the poles of the ecliptic, is called its latitude, 
and its angular distance measured on the ecliptic east- 
ward, from the equinox whence right ascension is 
reckoned is termed its longitude. Thus, in Fig. 20, where 
rLE represents the ecliptic, P 1 its north pole, P l K° a 
great circle passing through Aries, and P J SL, a great 
circle passing through the star at S, SL is the latitude 
of the star, that is, its distance from the ecliptic measured 
on the great circle P l SL. Since the arc P*SL is ninety 
degrees, if SL is thirty degrees, the latitude of the star is 
thirty degrees north. The longitude of the star is °fL ; 
the angular distance from Aries measured on the ecliptic 
to the great circle P *SL passing through the star. If T L 
is thirty-Jive degrees, then the longitude of the star is 
thirty-five degrees. 

75. The Signs. The ecliptic is divided into twelve 
equal parts, called signs, each sign occupying in the 
heavens, an extent of thirty degrees; within these divi- 
sions, are situated certain conspicuous clusters of stars, 
termed constellations, which in the infancy of Astronomy, 
-eceived particular names, and these names were also 
given to the signs. The following are the names and 
characters of the signs, north of the celestial equator, be- 
ginning at the vernal equinox, 

ARIES, The Ram, °f CANCER, The Crab, £3 

TAURUS, The Bull 8 LEO, The Lion, & 

GEMINI, The Twins, LT VIRGO, The Virgin, TTQ. 

The next six the names and characters of those 
south of the celestial equator, 

L1DR A, The Scales, =£= CAPRICORNUS, The Goat, . . . . V5 

SCORPIO, The Scorpion, ^l AQUARIUS, The Water Bearer, /& V 

SAGITTARIUS, The Archer,. . . t PISCES, The Fish, K 

76. Zodiac. The Zodiac is a belt of the celestial 
sphere extending eight degrees on each side of the eclip- 

How is the ecliptic divided 1 What is the extent of each sign 1 What are situated 
within these divisions ? Give the names of the signs? Which are north and which 
*outh of iho celestial equator ? What is the Zodiac, and why is it so called J 



REFRACTION. 55 

tic. It is so called from the Greek word zodia mean- 
ing figures of animals because they symbolize most of 
the signs of the ecliptic ; also called the signs of the 
zodiac. 



CHAPTER IV. 

OP REFRACTION AND PARALLAX. 



77. In the last chapter we explained the methods of 
determining the position of the heavenly bodies by meas- 
uring their angular distances from certain great circles 
of the sphere. 

In order, however, that their places may be fixed with 
precision, two important corrections are necessary, one 
to be applied in the case of the fixed stars, and both 
when the bodies observed are comparatively near the 
earth, as for instance, the sun and moon. The question 
may be asked, why are these corrections indispensable ? 
The reply is ; First, that owing to the action of the at- 
mosphere upon the rays of light, a star is seen out of its 
true place in every position but one ; Secondly that a 
like displacement occurs when a body not very remote, 
as the moon for instance is observed at the same instant 
of time from different points of the earth! s surface. The 
first displacement is caused by refraction 1 the second by 
'parallax. 2 

78. Kefraction. When a ray of light emanating 
from any object passes obliquely out of one medium 3 

1. Refraction. From the Latin refractus, broken. The deviation ol * 
line from its original course. 

2. Parallax. From the Greek parallasso. To change one place for 
another. 

3. Medium. This word here means any thing through which light 
passes. Thus if we look at a star the atmosphere is the medium through 
which we see it, and is so called because it is in the middle between the 
eye and the star. Medium is the Latin word for middle. 

What have been explained in the last Chapter t How many important corrections are 
necessary to fix with precision the place of a heavenly body 1 What effect has the at- 
mosphere upon the rays of light ? How is the second displacement caused 1 What i» 
refraction 1 What parallax 1 Explain refraction. 

3* 



56 THE EARTH VIEWED ASTRONOMICALLY. 

into another of different density, it is refracted or bent 
out of its original course, and when it reaches the eye 
the object is seen in the direction of the last refracted ray. 

In passing out of a rarer into a denser medium, the ray 
is turned towards the perpendicular to the surface of the 
medium ; the latter being drawn through the point where 
the ray strikes the surface. Now the atmosphere is a 
transparent medium, enveloping the globe and gradually 
decreasing in density from the surface of the earth 
upwards ; as the light from all celestial objects reaches 
us through this medium, it necessarily suffers refraction, 
and these radiant bodies are therefore seen by us as out 
of their true place. 

The angular distance between the true and apparent 
place of a heavenly body, is its astronomical refraction. 

79. Thus, if E, Fig. 21, represents the earth, Z the 
zenith, and 1, 2 ; 2, 3 ; 3, 4, different strata of the atmos- 
phere, decreasing in density from 1 to 4, a ray of light 
proceeding from the star S, and meeting the exterior 
stratum of the atmosphere at 4, will be successively re- 
fracted in the directions 4, 3 ; 3, 2 ; 2, 1, towards the per- 
pendiculars 4a, 3b, 2c ; so that a spectator at 1 will not see 
the star S in its real position, at S, but above it in the direc- 
tion 1-2 S*. The angle SIS 1 is its astronomical refraction. 

80. The direction of the ray in its passage through 
the air is constantly varying, since the density of the at- 
mosphere changes by imperceptible degrees. Its course 
will not therefore be accurately represented by the 
broken line 4, 3, 2, 1, but by a curved line taking the same 
general direction passing through the points 4, 3, 2, 1, and 
concave to the surface of the earth. 

81. Variation op Kefraction in respect to Alti- 
tude. When a ray of light passes out of one medium 
into another, the more obliquely it strikes the surface of 
the second medium the more it is refracted^ and if it falls 
upon it perpendicularly the ray is not refracted at all. 

82. "Now the light from a star strikes the atmosphere 
at the greatest possible obliquity, when the luminary is 

In what direction is an object seen. In passing out of a rarer into a denser medium, 
flow is the ray bentl What is said respecting the atmosphere ? What is Astronomical 
efraction. Explain from figure. Why is the course of the ray a curved and not a broken 
line t When is a ray of light most refracted 1 Whec not at all 1 



VARIATION OF REFRACTION, &C. 



57 



upon the horizon. This obliquity continually dimin- 
ishes with the altitude. At the zenith it is nothing, for 



FIG. 21. 




REFRACTION. 

ll.<5 rays of a star in the zenith fall perpendicularly 
upon the atmosphere. The refraction is therefore great- 
est at the horizon, and constantly decreases with the alti- 
tude, until at the zenith it becomes nothing. The follow- 
ing table exhibits the amount of refraction at different 
altitudes. 

APPARENT ALTITUDE OF THE RADIANT BODY BEING THE AMOUNT OF REFRACTION Tl 

'0 at the horizon, 33" 50" 

1° 24' 25" 

3° 14' 35" . 

10° 5' 20" 

— *20° 2' 39" 

44° 1> 

62° 31" 

71° 20" 

83° 7" 

90° at the zenith, 

It will be seen by a simple inspection of the table 

In what position of a heavenly body are its rays most refracted ? Where i» it seen in 
its true place, Give the table of altitudes and corresponding refractions ? 



58 THE EARTH VIEWED ASTRONOMICALLY. 

that the decrease of refraction is not by any means 
uniform, for the changes are extremely rapid near the 
horizon but proceed very slowly as we approach the 
zenith. * 

83. The Effect of Refraction on the Position 
f Heavenly Bodies. Kefraction causes a body to be 

seen above its true place. Thus, in Figure 21, the 
observed star, if there was no refraction would be seen 
by the spectator in the direction 1 S ; S being its true 
] lace, but owing to the refraction caused by the atmos- 
] here, it is seen at S 1 nearer the zenith. It has there- 
fore been elevated by refraction through the angular dis 
lance SIS 1 measured on a great circle perpendicular to 
the horizon. Refraction, therefore, increases the altitudt 
of a heavenly body, or what is the same diminishes its 
zenith distance. The correction for refraction must 
therefore be subtracted from its apparent altitude in order 
to obtain the true altitude. 

84. On Declination and Right Ascension. The 
displacement produced by refraction, affects the declina- 
tion and right ascension of a heavenly body. If an 
observer stationed at the equator, were to take the alti- 
tude of any star on the meridian, either north or south 
of the zenith, on account of refraction the star would be 
seen nearer the celestial equator than it actually is. Its 
declination would therefore be diminished. If the star 
observed were in the east upon the celestial equator, re- 
fraction would carry it along the celestial equator nearer 
the vernal equinox than its real position, and would 
therefore diminish its right ascension, but if the star was 
in the west it would be carried by refraction from the 
vernal equinox, and thus its right ascension would be 
increased. 

85. An observer at either pole of the earth would see 
the horizon coinciding with the celestial equator and at 
these stations, refraction would consequently increase 

Are the changes in refraction from the horizon to the zenith uniform ? Where 
are they most rapid 1 Where slowest 1 Is a heavenly body seen above or below its true 

Elace, when its light suffers refraction "? Explain from figure How is the altitude of a 
eavenly body affected by refraction 1 What use must be made of the correction for re- 
fraction in order to obtain the true altitude 1 Explain in what manner the astronomical 
refraction of u heavenly body would affect its right ascension and declination at the equs 
tor ; when on the meridian or the celestial eauator ? How at the poles ? 



&c. 59 

the declination of every star in the visible heavens. 
Their right ascension would be unaffected. 

In all latitudes from the equator to the poles, the dis- 
placement caused by refraction is in a direction oblique to 
the celestial equator, unless the heavenly body is in the 
meridian. It therefore affects with this exception both 
right ascension and declination, and the same is true in 
respect to the refraction of all stars observed at the 
equator, which are not situated either on the meridian 
or the celestial equator. 1 

86. The amount of refraction at the horizon is about 
thirty -four minutes, which is a little greater than the 
angular diameters of the sun and moon. At their rising 
and setting, therefore, these bodies come entirely into 
view when they are actually below the horizon ; an ex- 
traordinary instance of refraction is said to have oc- 
curred in the year 1597, at Nova Zembla, in 1ST. Lat. 
75 i°, the sun appearing above the horizon, when it was 
really seven times the length of its apparent diameter 
below it. The effect, therefore, of refraction upon the sun 
is to increase the length of the day. 

87. This point is illustrated by Figure 22, where E 
represents the place of the observer on the earth, and 
S the true position of the sun when he appears just 
above the horizon H l H at S 1 . The ray LdE coming 
from the lower edge of the sun reaches the spectator at 
E in the direction dE, and he sees the lower edge in the 
direction of EdL 1 . In the same manner the ray Ed E, 
proceeding from the upper edge of the sun comes to the 
spectator in the direction d^, and the upper edge is 
seen in the direction Ed l R l . Thus, the entire body of 

1. This must be so, for a displacement which takes a direction oblique 
to the equator can be resolved by the laws of mechanics into two displace- 
ments, one of which takes place in a direction parallel to the equator, and 
the other perpendicularly to or from it. Theirs* affects right ascension, 
the second declination. 

How at all latitudes between the equator and the poles 7 How ai the equator when me 
observed stars are neither in the meridian nor the celestial equator 1 How does the amount 
of refraction at the horizon compare with the angular diameters of the sun and moon t 
What singular phenomenon occurs at the rising and setting of the sun and moon 1 What 
extraordinary instance of refraction was once obser ed at Nova Zembla? What influence 
has refraction on the length of the day. Explain figure 22 



60 



THE EAETH VIEWED ASTRONOMICALLY. 



the sun is actually seen above the horizon H'H, at S l , 
when the orb is really below it at S. 



FIG. 22. 




EFFECT OF REFRACTION UPON THE SUN WHEN ON THE HORIZON. 

88. All the other heavenly bodies are similarly af- 
fected, the time of their rising being accelerated, and 
that of their setting retarded. The period of the visi- 
bility of the stars above the horizon, is therefore in- 
creased by refraction. 

89. Effraction influenced by the Temperature 
and Pressure of the Atmosphere. It has been 
found that the varying pressure and temperature of the 
atmosphere at the place of observation, produce a change 
upon the refraction for any given altitude. Astrono- 
mers for this reason in preparing tables of refractions 
for use, give due weight to the indications of the ther- 
mometer and barometer, in order to insure correctness 
in the results. Thus in the tables given in Art. 82. 
che estimates are made upon the supposition that the 
height of barometer 1 is thirty inches, and that the tem- 
perature is 47° Fah. 

90. Of Parallax. The apparent angular displace- 
ment of a body caused by being seen from different 
points of observation is its parallax. 

Thus, if two persons A and C, placed at two adjacent 
corners of a room were to look at a ball situated in the 
centre of the room, A would see it in a line with the op- 
posite corner nearest to C, and C in the direction of the 
corner nearest to A; and the angle made by the two lines 

1. The barometer is aji instrument that measures the pressure of the 
atmosphere. 

What effect has refraction on the rising and setting of all heavenly bodies ? Does it 
lengthen or shorten the period of their visibility 1 Do the temperature and pressure of the 
atmosphere influence refraction 1 What is se\d respecting the construction of the taMei 
in Art 83 ? What is parallax 



OF PARALLAX. 



61 



of visible direction, would in a general sense be the 'par- 
allax of the ball. Thus in Fig. 23, where the lines 1, 2 ; 
2, 4 ; 2, 7 ; &c, represent the outline of the room, let B be 
the ball, A the place of the eye of one spectator, and C 



FIG. 23. 




PARALLAX EXPLAINED. 



the position of that of the other. The ball would be 
seen by the first in the direction ABX, and by the 
second, in the direction OBY, and the angle ABC would 
be the 'parallax of the ball, or the angular displacement 
that it suffers by being viewed from the two stations 
A and C. 

91. Now if two astronomers, one at St. Petersburg, 
and the other at the Cape of Good Hope, were to 
observe the moon at the same absolute moment of time, 
and fix her position in the heavens, making allow- 
ance for refraction only, it is evident that their results 
would not be exactly alike ; because the two observers 
behold the moon from different points in space, and 
would see her in different places on the celestial sphere ; 
and such would be the case with any observers who 
were not making their observations from the same spot. 

Explain from figure. Relate what is said respecting the observations upon the mono. 
taken from different stations? Why must allowance be made for parallax in astronom' 
«at observation* 1 



62 



THE EARTH VIEWED ASTRONOMICALLY. 



Allowance must therefore be made for this angular dis- 
placement or parallax in order to prevent confusion in as- 
tronomical calculations ; and as in the case of longitude 
we must have some standard meridian whence to reckon 
the degrees of longitude, so in parallax we must have 
some standard station, from which all celestial objects are 
supposed to be viewed. This imaginary station is the 
centre of the earth, and the true position in the sky of any 
heavenly body, is determined by an imaginary line 
drawn from the centre of the earth to the centre of the body, 
and prolonged to meet the starry vault. 

92. Parallax. How measured. The angle con- 
tained between two lines, drawn from the centre of the 
body, one to the eye of the observer, and the other to the 



FIG. 24. 




PARALLAX OF A HEAVENLY BODY. 



centre of the earth, is the measure of the parallax of the 
body. 

Thus, in Figure 24, where the curve PEZC represents 

Where is the standard station from which all celestial objects are supposed to be seen? 
How is the true position in the heavens of a planet or planetary body determined 1 How if 
oarallax measured ? Explain from figure. 



HORIZONTAL PARALLAX. 63 

a fourth part of a celestial circle extending from the 
'lorizon P to the zenith Z,M,M', M 2 , M 3 the moon at dif 
lerent altitudes, C, the centre of the earth, and A the 
place of the observer ; AMC is the angle of parallax 
when the moon is in the horizon, AM 1 ^ the same when 
she is fifty-five degrees above the horizon, and AM 2 C 
when she is near the zenith. 

93. Variations in Parallax — Effect of Alti- 
tude. It is evident from the inspection of the figure 
where the arc M, M 1 , M% M 3 , represents a part of the 
moon's orbit that the parallax is greatest when the moon 
is on the horizon, and gradually diminishes until it 
becomes nothing at the zenith. At the zenith there can 
be no parallax, because the lines drawn from the centre 
of the moon at M 3 to the place of the observer at A, and 
to the centre of the earth C, make no angle with each 
other but form one line ; the moon must therefore be 
seen at the same place in the starry heavens ; viz. Z, 
whether viewed from A or C. 

What has been just stated in respect to the moon is 
true also of every other heavenly body, whose parallax 
can be measured ; viz., that the parallax is greatest when 
the body is at the horizon, and gradually diminishes with 
the altitude, becoming nothing at the zenith. 

94. Horizontal Parallax. The horizontal parol 
lax of a body is its parallax when seen upon the horizon. 
Thus, in Fig. 24, the observer being at A, the hori- 
zontal parallax of the moon is the angle AMC ; an angle 
formed by drawing from the centre of the body whose 
parallax is sought two lines, one to the place of the spec- 
tator touching the earth, and the other to the centre of 
the earth. 

95. Effect of Distance. The amount of parallax 
is influenced by distance ; the greater the distance the less 
the parallax, and the smaller the distance the greater the 
parallax 1 . This is clear from a glance at Fig. 24, where 

1. When this relation exists between two quantities they are said to be 
inversely proportional to each other. 

When ii the parallax greatest? When does it become nothing? Why uoes it' 
What is horizontal parallax 1 Explain from figure. Are the statements just made appli- 
cable to every other heavenly body having a parallax that can be measured ? Is the amouni 
. f narallax influenced bv the distance of a bodv 1 Giv# the rule. 



tf4 THE EARTH VIEWED ASTRONOMICALLY. 

S lepresents a planet more distant from the earth then 
the moon at M l , but having the same altitude; and SS 
the path of the planet. Now the parallax of the planei 
S is the angle ASC which is evidently smaller than the 
angle AM'C, which is the parallax of the moon at M 1 . 

96. Since the parallax decreases with the increase 
of distance, it results that when a body as a fixed 
etar is situated very far from the earth the parallax 
becomes so small that it is impossible to measure it ; a 
fixed star will therefore appear to occupy the same place 
in the heavens, whether viewed from the centre or the 
surface of the earth ; indeed the same will be true if it 
is even observed from opposite sides of the earth's orbit 
around the sun. 

97. Effect of Parallax upon the true position 
of a Heavenly Body. The true position of a heavenly 
body, being that which it would have if seen from the 
centre of the earth, it is evident that the effect of par- 
allax is to depress a body below its true position. In 
Figure 24, the true position of M, in the celestial vault 
is P, since it would appear at P if the eye was at C; but 
the spectator at A, sees the moon at the place L in the 
celestial vault, the luminary being depressed, the extent 
of the arc of parallax PL. The amount of depression 
at M 1 is P l L», and at M 2 it is P 2 L 2 . 

We thus see that parallax decreases the altitude of a 
heavenly body, and must therefore be added to the ap- 
parent altitude, in order to obtain the true altitude. 

98. On Declination and Eight Ascension. At the 
poles of the earth the effect of parallax, to its whole ex- 
tent, would be to lessen the declination of a heavenly 
body, since it would cause it to appear nearer the celes- 
tial equator (which here coincides with the horizon) than 
its true position. At the equator of the earth the entire 
influence of parallax, if the body was in the east would 
be to increase its right ascension, and if in the west to 
diminish it. If it was on the meridian the declination 

Explain from figure. What is said of the parallax of the fixed stars ? What is the ef 
feet of parallax upon the true position of a heavenly body ? Explain from figure. What 
effect has parallax upon the altitude, and how must the correction for altitude be em- 
ployed 1 What is the effect of parallax upon declination and right ascension 1 At th« 
poles 1 



PARALLAX, ITS VALUE. 65 

only would be increased, but in all other directions not 
named, parallax would influence both right ascension 
and declination. At all latitudes between the poles and 
the equator, right ascension and declination would like- 
wise be both influenced by parallax, except when the 
body was in the meridian when the declination only 
would be affected. In a word, the displacement caused 
by parallax in regard to altitude, right ascension, and 
declination, is exactly the reverse in direction to that 
which happens from refraction, and which has already 
been explained. 

99. Parallax — Its value. The determination of 
the amount of parallax belonging severally to distant 
heavenly bodies is of the utmost importance in astro- 
nomical researches. By its aid we can ascertain the dis- 
tances of the sun, planets, and comets; and knowing 
their distances we can tell their actual magnitudes, their 
densities and the quantity of matter they separately con- 
tain, together with the extent of their orbits, and the 
swiftness of their speed. 

Still further, having by means of the parallax of the 
sun obtained his distance from the earth, this distance 
becomes the measure by which the astronomer gauges the 
remoter heavens, and discovers the amazing distances of 
the fixed stars. Without the key afforded by parallax 
his efforts would be checked at the beginning, and a vast 
field of knowledge would remain forever unexplored. 

100. More mathematical knowledge is required to un- 
derstand the method by which the parallax of a body 
is ascertained, than the majority of students for whom 
the work is prepared are expected to possess. 

For the benefit of those who have a knowledge of Trigonometry, the fol- 
lowing demonstration is annexed. Let C be the centre of the earth, 
PP 1 a portion of the terrestrial meridian passing through the stations of 
two observers, one at P, the other at P 1 . ZUOLZ 1 the corresponding 
celestial meridian, Z the zenith of the observer at P and Z 1 the zenith 
of the observer at P 1 . M represents the moon, L the place in the 
heavens at which she is seen by the observer at P, and L 1 , her place as 
beheld from P ; , her true place being O the direction in which she is 
seen from the centre of the earth. Now to find the parallax at P, viz., 

At the equator and at intermediate latitudes 1 Compare the effects of refraction and 
parallax in the above particulars "? Why is the knowledge of parallax imoortant to tha 
astronomer 1 



6ft THE EARTH VIEWED ASTRONOMICALLY 

CHAPTER Y. 

OF THE MEASUREMENT OF TIME. 

101. Transit Instrument. Having now acquired 
a knowledge of the circles of the celestial sphere, and 
the manner of fixing the positions of celestial bodies in 
the sky, we are prepared to investigate more minutely 
the rotation of tJie earth on . its axis. We have discov- 
ered the fact of the rotation, but h ,ve not yet ascertained 
whether the earth moves faster at one time than at an- 
other. This point, however, is readily ascertained by the 

CMP. Taking the figure as drawn, we have first, the latitudes of the two 
stations which gives us the angle PCP 1 , consequently in the isosceles tri- 
angle P a CP we have the two lines PC, P'C, each a radius of the earth, and 
the included angle to find the other angles and the side PP 1 . Now the 
zenith distances of the moon, as seen from both stations, cm be measured ; 




tney are the angles ZPL and ZT'L 1 ; therefore we know their supplements 
to wit, LPC and L'P'C. Taking away from these respectively, the angles 
CPP 1 and CPT, we have remaining the angles LPP 1 and LTT. Con- 
sequently in the triangle MPT we have the side PP 1 , and all the angles to 
find the other two sides MP and MP 1 . Now taking the triangle MPC we 
have the side MP (just found) CP a radius of the earth, and the angle M 
PC the supplement of the moon's zenith distance, to find the other parts 
one of which namely CMP is the parallax. In this manner the parallax 
of Mars, was obtained by Lacaille and Wargentin, the former being sta- 
tioned at the Cape of Good Hope, the latter at Stockholm. If the parallax 
nt anv altitude is obtained, the horizontal parallax can be derived from it ; 
the parallax varying as the sine of the zenith distances. This method is not exact 
enough for the sun, owing to his great distance. His true horizontal parallax is 
otherwise found, (Arts. 462-3,) and his distance is then computed by it. 



TRANSIT INSTRUMENT, 



67 



aid of i J accurate clock, and a peculiar kind of telescope 
called a transit instrument Fig. 25 ; within this instru- 
ment is placed a system of wires like those shown at ac f 



FIG. 25. 




TRANSIT INSTRUMENT. 



Fig. 26, one horizontal and five vertical: the latter being 
parallel to each other, and separated by equal intervals - 1 



FIG. 26. 




1. See note 1, to Art. 103. 



Of what iloes Chapter IV treat 1 How can we ascertain that the ea'th moves 
formly on h*r axis? Describe »he transit instrument i 



68 THE EARTH VIEWED ASTRONOMICALLY. 

1, 2 ; 2, 3 ; 3, 4; &c. These wires are situated in the 
focus 1 of the eye-glass atF, Fig. 25, their plane being at 
right angles to the imaginary line 2 passing lengthwise 
through the centre of the telescope, the central vertical 
wire C, cutting this line at right angles. 

102. The telescope is provided with a horizontal axis 
upon which it rests, and it must be so adjusted, when 
properly arranged, that the central wire shall move with 
perfect accuracy in the plane of the meridian, as the in- 
strument revolves on its points of support. This is the 
great object sought in its adjustment, and to guard 
against the slightest deviation, the pillars, P, P 1 , upon 
which the ends of the horizontal axis rest, are built 
of the firmest masonry, and detached from the other 
parts of the building where the transit instrument is 
placed, so that they may not be affected by any motion 
of the edifice. Levels are attached to the instrument 
to aid in its adjustment. Measurements are taken upon 
a graduated circle 3 fixed to the axis. 

103. Of the Time Occupied by the Earth in Per- 
forming one Rotation. — How Determined. Let us 
now observe the astronomer as he proceeds to investi- 
gate the problem of the earth's rotation on her axis. 
Seated in his observatory, with his telescope and clock 
properly adjusted, he selects for his sky -mark some 
bright fixed star near the meridian. He watches it 
closely, and soon the earth, as it rotates towards the 
east, brings the telescope up to the star. At the moment 
the latter is upon the meridian, the middle vertical wire 
of the instrument cuts the star exactly in two, and the 
astronomer notes the time by his astronomical clock ; we 
will suppose it to be eight. During the rest of the night 
and the succeeding day, the astronomer, with his obser- 

1 . The focus is that place in front of the eye-glass, where the wires can 
be seen distinctly, when a person is looking through the telescope. 

2. This line is called the line of collimation, and is imagined to join tho 
centres of the object and eye-glasses. 

3. A graduated circle is a metallic circle, the circumference of which m 
divided into degrees, minutes, and fractions of a minute. 

What is the great object sought in the adjustment of the transit instrument ? How are 
measurements taken ? Describe in full haw the time occupied by the earth in perform- 
ing one rotation is determined 



TIME OCCUPIE/J BY THE EARTH, &0. 69 

vatory and instruments rotating with the earth, passes 
star after star in succession, and as eight o'clock ap- 
proaches, the observed star of the preceding evening is 
seen again near the meridian. The astronomer is at his 
post, and again the central vertical wire 1 cuts the star 
exactly in two, showing that the earth has completed 
one rotation ; and at this identical moment the clock in- 
dicates with the utmost precision the hour of eight. 
Twenty-four hours have elapsed since the first observa- 
tion ; this then is the period of time occupied by the 
earth in performing one entire rotation. Such observa- 
tions have been made repeatedly, both upon the same 
star and upon different stars, and at stations widely sep- 
arated, and the result has been found to be invariably 
the same. Centuries may intervene between two series 
of observations, and yet the results are identical ; we thus 
arrive at the conclusion that the interval of time elapsing 
between two successive transits* of a fixed star, and which 
measures one entire revolution of the earth,' is unchangea 
hly the same. 

104. Having found that the earth rotates once every 
twenty-four hours, a question arises, is this motion uni- 
form? That is, does the earth rotate through equal 
spaces in equal times, performing half a rotation in 
twelve hours, a quarter in six hours, and so on ? This 
is found to be the case. If the angular distance between 
two stars is fifteen degrees, or one twenty -fourth part 
of one entire rotation, i. e., three hundred and sixty de- 
grees ; the time that elapses from tne transit of the first 
star to the transit of the second, is exactly one hour, no 
matter at what time of the day the observations are taken. 
The earth, therefore, passes through one twenty-fourth 

1. To avoid errors, the astronomer marks the time when the star crosses 
each of the five vertical wires, and then, by taking an average of these times 
he can determine with greater precision when the centre of the star is in 
the meridian, than if he noted its passage only across the central wire. 

2. Transit. The transit of a star is the moment of its passage across the 
meridian when it is cut exactly through the centre by the central vertical wire 
of the transit instrument. Transit, from the Latin word transitus, & passage. 

Is this period changeable 7 Is the motion of the eartr on its axis uniform 1 How i* 
it proved ? 



70 THE EARTH VIEWED ASTRONOMICALLY. 

part of a rotation in one twenty-fourth part of a day, and 
this is true for all other divisions, whether greater or 
smaller. Half of a rotation is performed in half a day. 
the one hundredth part of a rotation in the one hun- 
dredth part of a day, and so on. 

105. Standard Unit of Time. The period of the 
earth's rotation on its axis is the universally acknowl- 
edged unit of time, since it is the only natural marked 
division of time which continues unaltered from age to 
age. All other periodical motions of the heavenly 
bodies are subject to change, but the difference in the 
length of the natural day, as determined by a comparison 
of the earliest and the latest observations, is inappreciable. 
The different periods of time in common use all date 
from this. Weeks, months, and years are reckoned by 
days and fractions of a day, while hours, minutes, and 
seconds, are divisions and sub-divisions of the day. 

106. Of the Sidereal and Solar Day. The sidereal 1 
day is the length of time that elapses between two suc- 
cessive transits of the same fixed star across the meridian, 
in other words, the period of the earth's rotation. The 
solar 2 day is the time that elapses at any place between 
two successive transits of the sun across the meridian of 
that place ; or, as it is commonly expressed, the time 
that intervenes between noon of one day and noon of 
the next. The solar day is aoout four minutes longer 
than the sidereal, and the causes of this difference we 
will now proceed to explain. 

107. We must bear in mind; First, that the earth 
moves around the sun from west to east, rotating also at 
the same time on its axis from west to east. Secondly, 
that the axis never changes its direction, but constantly 
points north # and south. Thirdly, that the half of the 
earth which faces the sun is illuminated, while the other 
is veiled in darkness. These facts are illustrated in 

1. Sidereal, from sidera, the Latin word for stars. 

2. Solar, from Sol, the Latin word for the sun. 

What is the standard of timel Why is this division of time adopted as a standard 1 
What is said of weeks, months, and years? Hours, minutes, and seconds? Wlat is 
meant by the term sidereal day ? What by solar day ? Which is the longest ? What 
iiiow *.o be explained ? What three things must we bear in mind ? 



OF THE SIDEKEAL AND SOLAR DAY 



71 



Fig. 27, where S represents the sun, and the globes, 
A, B, C, and D, fcur positions of the earth, three months 
apart; viz., at the vernal equinox, (A,) the summer solstice, 



FIG. 27 




SOLAR AND SIDEREAL DAY. 

(B), the autumnal equinox, (C), and the winter solstice 1 , 
(D). Here, in the first place, the earth is seen, as shown 

1. The vernal equinox occurs on the 20th of March; the summer sol- 
stice on the 21st of June : the autumnal equinox, on the 23d of Sep 
♦ember ; and the winter solstice, on the 21st of December. 
4 



72 THE EAETH VIEWED ASTRONOMICALLY. 

by the arrows, rotating from west to east, ! (W to E,) 
while at the same time it revolves about the sun in the 
like direction. Secondly, its axis is unchanged in posi- 
tion, as shown by the way in which the meridians con- 
verge. Thirdly, the hemisphere towards the sun is illu- 
minated while the other is in darkness. 

108. Now it is noon at any place when an imaginary 
plane, called the meridian plane, passing through the 
centre of the sun, and the north and south poles of the 
earth, also passes through this given place, dividing the 
illuminated hemisphere into two equal parts. And this 
must be the case, for the place has enjoyed the sunshine 
during the time the earth, in its daily revolution, has 
been describing the half of the illuminated part towards 
the east, and will enjoy it for the same space of time while 
describing the half towards the west. Thus, the earth 
being at A, it is noon, or twelve o'clock, at the place, 
N, which is in the position just described. For the time 
the earth occupied in revolving from the position E, to 
that of 1ST, constitutes the half of the day 2 from sunrise 
to noon, while that employed in rotating from the po- 
sition IS", to that of W, is that half which is included 
between noon and sunset. As the earth is here at the 
vernal equinox, each half day is six hours long. 

109. We will now suppose that it is noon at N, on 
the day of the vernal equinox ; to-morrow, when the 
earth has exactly completed one rotation, it will not be 
noon at N, because the earth has advanced in her path 
around the sun about one degree from the vernal equi- 
nox. This orbitual motion 3 has caused the boundaries 
of the illuminated hemisphere to shift around to the 
east, through nearly one degree, and the meridian plane 
has also moved eastward to the same extent. The earth 
must, therefore, rotate over and above one entire revolu- 
tion through the same angular space of nearly one degree 

1. For an explanation of the term, rotating from west to east, see Art. 
134. 

2. The word day is here used as opposed to night. 

3. Orbitual motion, motion in her orbit around the sun. 

Illustrate by the figure. When is it noon nt any place 1 vVhy so ? Explain from Fig- 
27. Why is the solar day longer than the sidereal ? 



OF THE SOLAR AND SIDEREAL DAY. 



73 



before it brings the place N, into such a position that 
equal portions of the illuminated hemisphere will be 
immediately east and west of it. Then, and only then, 
has N reached the meridian plane, and the time of noon 
arrived. As the earth revolves through three hundred 
and sixty degrees in twenty-four hours, it passes through 
one degree in four minutes, so that in round numbers 
we may say that the solar day is about four minutes 
longer than the sidereal 

110. This subject is illustrated by the following dia- 
gram, Fig. 28, where S represents the sun, and E, E, 

FIG. 28. 




SOLAR AND SIDEREAL, DAV. 



How much longer is it 7 Explain from Fig. 28. 




74 THE EARTH VIEWED ASTRONOMICALLY. 

the earth in two positions of its orbit ; the dark semi- 
circles are sections of the unenlightened hemispheres, 
and the light semi-circles, sections of the enlightened 
hemispheres. In position 1, it is noon at 1ST, because there 
are equal portions of the illumined hemisphere on the 
east and west side of it. But on the next day, when the 
earth has made one complete rotation, and has in the 
meanwhile also moved along in its orbit, CD, to position 
2, it will not then be noon at N, for the meridian plane 
now passes through N 1 : the earth will have to re- 
volve on its axis until N has arrived in the position N 1 , 
before it will be noon at N, and the time occupied in 
describing the arc, NN 1 , will be the excess of the solar 
above the sidereal day. 

111. The difference in the length of the solar and 
sidereal day may be explained by the motions of the 
hands of a watch. Calling the time made by one revolu- 
tion of the minute hand a sidereal day, a solar day may 
be compared to the extent of time that elapses from the 
instant the hour and minute hands are together, to the 
next time they are again in that position ; a period man 
tfestly longer than the first, since the minute hand has 
not only to make one revolution, but must also catch up 
with the hour hand, which has all the wHile been ad- 
vancing. 

112. Another view may be taken of this subject. A 
glance at Fig. 27 shows us, that reckoning from A the 
limits of the illuminated hemisphere at the summer sols- 
tice have shifted round along the plane of the ecliptic 
one quarter of a circumference, at the autumnal equinox 
one half a circumference, at the winter solstice, three quar- 
ters of a circumference ; and when the earth has arrived 
at the vernal equinox again, the bounding circle divid- 
ing the illuminated from the unilluminated hemisphere, 
has made one entire revolution; the meridian plane 
changing round in the same manner. 

113. Now, if we could imagine that on the day of the 
vernal equinox, just before it is noon at N, the earth 

Explain the difference between solar and sidereal time. Illustrate by the motion* of the 
hands of a watch. Illustrate the subject still farther by the aid of Fig. 27. 



INEQUALITY IN THE LENGTH OF SOLAR DAYS. 75 

could be at once transported to the position it occupies at 
the autumnal equinox, (C) the place N, would be instan- 
taneously buried in the gloom of midnight ; since the 
limits of the illuminated hemisphere, and the meridian 
plane, would shift r*und half a circumference, and the 
earth would have to make almost half a rotation before N 
would again enjoy noon. So that the interval between 
noon on the day before the vernal equinox, and the noon 
of the day after, would, on this supposition, be very 
nearly thirty-six hours. But the earth makes no such 
rapid transition in passing from the vernal to the autum- 
nal equinox, but occupies about one hundred and eighty- 
six days 1 in this journey; the bounding circle of the il- 
luminated hemisphere and the meridian plane moving 
a little round every day, and completing half a circum- 
ference, in circular motion or twelve hours of time (one hun- 
dred and eighty degrees,) in the course of nearly one 
hundred and eighty-six days. 

This daily motion of the mericfian plane is, therefore, 
about one degree* or nearly four minutes of time,* and 
constitutes the excess of the solar above the sidereal day. 

114. Inequality in the length of the Solar 
L>ays. In the previous explanations we have consid- 
ered, for the sake of simplicity, that the solar days are 
of equal length, in other words, that the period of time 
comprised between noon of any one day, and noon of 
the next, is the same in every part of the year. But 
this is not so, for two reasons. 

1. One hundred and eighty-six days, more nearly one hundred and 
eighty-six and a half. The earth occupies only about one hundred and 
seventy-eight and a half days in passing from the autumnal to the vernal 
equinox. 

2. About one degree. 180° equals 10,800 / which, divided by 186 
give 58' or nearly one degree. The entire orbit of the earth, equal to 
three hundred and sixty degrees, is described in about three hundred 
and sixty-five days. The average daily angular motion throughout the 
whole year is found by dividing 360° equal to 21 ,600 / by 365, which give 
fifty-nine minutes, and a little over. 

3. Four minutes in time. This is obtained by dividing twelve hours by 
one hundred and eighty-six, which give nearly one-fifteenth of an hour, or 
four minutes. 

An the solar days of equal length ? State the first cause of their inequality. 



76 THE EARTH VIEWED ASTRONOMICALLY. 

115. First, because the earth, not being always at the 
same distance from the sun, moves in different parts of 
its orbit with unequal velocities — advancing most rap- 
idly when it is nearest the sun, and with its least velocity 
when most remote from this luminary. O nsequently, 
the daily amount of change in the position Df the meri- 
dian plane is variable throughout the year, and, there- 
fore, the space of time which the earth must rotate, in 
order to complete a solar day, will also be variable. 
The greatest difference in length between the solar and 
sidereal day, is two hundred and sixty-six ^seconds ; the 
least two hundred and fifteen seconds ; and the average for 
the year, two hundred and thirty-six seconds, or nearly 
four minutes. 

116. Secondly, time is not reckoned on the ecliptic, but 
on the equator, and since the plane of the former is in- 
clined to that of the latter, it follows that anv given 
angular motion of the earth along the ecliptic does not 
always give the same amount of angular motion on the 
equator. In other words, a degree of longitude is not 
necessarily equal to a degree of right ascension. 

117. This is evident from the inspection of Fig. 29, 
where C represents the position of the earth at the ver- 
nal equinox ; N and S the north and south poles of the 
earth, MCB the equator, L the sun, and ECOZ a 
part of the earth's orbit. CO is an arc of longitude, of 
nineteen degrees extent, which the earth describes in 
passing in its orbit from C to 0, and CM is the corres- 
ponding 1 motion of the earth in right ascension, de- 
scribed in the same time. Now it is evident that CO is 
longer than CM, 1 consequently, when the earth has 
moved nineteen degrees in longitude from the vernal 
equinox, it has moved less than nineteen degrees in right 

1, Ares of longitude and right ascension are said to correspond when 
they are included between the planes of the same meridians. 

2. CO longer than CM — because CMO is a right-angled spherical tri- 
angle, CMO being the right angle, and the side opposite the right angle, in 
a right-angled triangle, is always greater than either of the other sides. 

What is the gteatest difference in length between the solar and sidereal day ? Wbat 
the least ? What the average "? State the second cause of the unequal lengths of the 
eoiar days. Explain from figure. State what is said respecting arcs of longitude and 
their corresponding arc of right ascension. 



MODES OF RECKONING TIME. 

« 

FIG. 29. 



77 



EAST 




WEST 



TIME RECKONED ON THE EQUATOR. 

ascension ; the same is here true of the daily arcs of lon- 
gitude, and their corresponding arcs of right ascension. 

118. From each equinox towards the next sol- 
stice, the daily arcs of longitude are at first greater 
than the corresponding arcs of right ascension ; then 
equal ; then less. And onward towards the next suc- 
ceeding equinox, the daily arcs of longitude differ 
from the corresponding arcs of right ascension. These 
variations necessarily produce corresponding changes 
in the length of the solar day. They are independent 
of those arising from the first mentioned cause, for they 
would exist, even though the earth moved in every 
part of her orbit with the same speed. 

119. Modes of Reckoning Time. The exigencies 
of society, and the refined calculations of science, have 
made it necessary that different modes of computing 
time should be adopted. Thus, we speak of apparent 

What is the effect of these variations 1 Would the length of the solar day be influenced 
> Ihese if the earth moved uniformly in her orbit 1 



78 THE EARTH VIEWED ASTRONOMICALLY. 

feme, mean solar time, 1 or civil time,* and astronomical 
time. 

120. Apparent time is the time computed from noon 
to noon by the successive returns of any place to its 
meridian. Since these successive periods (as we have 
seen) are of variable length, the apparent solar days, 
which are nothing but these successive periods, are also 
of unequal duration. 

121. Mean solar time is an arbitrary division of 
time, in which all the solar days are supposed to be of the 
same length, this length being found by dividing the 
whole amount of time in a solar year by the number of 
solar days in that period. Days of changing length 
would furnish an inconvenient method of reckoning for 
mankind, mean solar trme is therefore employed in the 
common affairs of life, and constitutes civil time. Under 
this usage, the mean solar day is made to consist of 
twenty-four hours, in order to avoid a fractional expres- 
sion for its length, which would happen if the sidereal 
day was divided into twenty -four hours. To compen- 
sate for this change, the latter is proportionally reduced 
in length. According to civil time the length of the 
mean solar day is, therefore, twenty-four hours, and 
that of the sidereal, twenty-three hours, fifty-six minutes 
and four seconds. The civil day commences at twelve 
o'clock at night, and is divided into two periods, of 
twelve hours each, reckoning from one to twelve from 
midnight to noon, and again from one to twelve from noon 
to midnight. 

122. Astronomical time is apparent time, and is em- 
ployed for scientific purposes. The astronomical day 
commences at noon 1 and terminates at noon on the next 

1 . Mean Solar Time. The word mean here signifies average. 

2. Civil Time. The legal time or that appointed by a government to 
to be used in their dominions. 

What is apparent time? What is mean solar time! What is civil time ? Why it 
mean solar time adopted as civil time 7 Under this usage, of how many hours does the 
mean solar day consist, and why ? What is the length of the sid« real day, that of the 
solar being reckoned at twenty-four hours ? When does the civil day begin, and how it it 
divided? What is astronomical time? When does the astronomical day begin 1 Of 
how many houn does it consist, and how is it reckoned ? 



EQUATION OF TIME. 79 

day. It consists of twenty-four hours, the hou * being 
counted from one to twenty -four. 

123. Equation of Time. The kind of ume em 
ployed by mankind for regulating the common concerns 
of life is, as we have stated, mean solar time, in which 
all the solar days are considered to be of equal length. 
The period of a day is artificially determined by clocks 
and watches, and they are usually made to keep mean 
time. Were such a clock to move with perfect accuracy, 
all the days of the year, as indicated by it, would be 
exactly of the same length. The length of the true 
solar day varies throughout the year, being sometimes 
greater, sometimes less than the solar day, and at certain 
periods equal to it. The difference between the length 
of the true solar day and the mean solar day at any time 
of the year, is the equation 1 of time for that date. 

124. If two clocks were taken, one of which kept 
true solar time, and the other true mean time, they 
would agree only on four days of the year, namely, 
April 15th, June 14th, September 1st, and December 
24th, at which times it would be noon by one of the 
clocks at the same moment it would be noon by the 
other ; throughout the rest of the year they would differ. 
Sometimes the true solar clock would be in advance 
of the other, and the sun would be said to be fast of the 
clock, and sometimes it would be behind, when the sun 
would be said to be slow of the clock. The difference 
in time between two such clocks at any period, would 
be the equation of time. 

The equation of time subtracted from the solar time, 
when in advance of mean time, and added when be- 
hind it, gives the true mean time. Thus, on July 4th, 
1852, the sun was slower than the clock by four min- 
utes and four seconds, and this amount must be added 

1 . Equation, a making equal. Equation of time is so called, because 
»vhen this quantity is added to, or subtracted from the true solar day, as 
the case may be, it makes it equal to the corresponding mean solar day. 

How is the period of a day artificially determined 1 What kind of time do they keep ? 
If a clock moved with perfect accuracy, how would the lengths of all the days of the 
year, as indicated by it, compare with each other ? What is meant by the term equation 
of time ? Give the illustration. The equation of time and the solar time being known 
how is the true me*'., time obtained ? Give examples. 

4* 



80 THE EARTH VIEWED ASTRONOMICALLY. 

be added to the solar time to make it equal to the 
mean time, at that date ; while on the 27th of Novem- 
ber of the same year, the sun was in advance of the 
clock, twelve minutes and two seconds, and this quan- 
tity must be subtracted from the solar time to obtain 
the mean time on the given day. The equation of 
time is greatest on the 3d of November, when it 
amounts to nearly sixteen minutes and eighteen seconds. 

125. The four epochs of the year when the true 
solar time agrees with the mean solar time, will not 
always happen upon the dates just given. One cause 
of the variation in the length of the solar days, is the 
unequal motion of the earth in its orbit — Art. 115. The 
earth now moves most swiftly in the beginning of Jan- 
uary, being then nearest to the sun, the equation of time 
becomes nothing at the dates above mentioned. But 
the period when the earth moves most rapidly is contin- 
ually changing, Art. 182 ; and in the course of ages it 
may occur at any time of the year ; and this change will 
effect a corresponding change in the dates when the 
mean and true solar time agree. 

126. Astronomical Clock — Sidereal Time— Error 
and Rate. The clock used in the observatory is a 
pendulum clock made with great accuracy, and possess- 
ing every arrangement to ensure regularity of motion. 
It is adjusted, as has been already explained, to keep 
sidereal time ; that is it divides the interval between 
two successive transits of a star into 24 hours. 

Sidereal time begins when the vernal equinox crosses 
the meridian, at which time the hands of the clock 
(if it is correct) indicate h m s . If this is not the 
case the clock is in error, and the amount of error is 
the difference between the true sidereal time and the 
clock time. The amount of error is not constant, but 
may vary from day to day, and this diurnal change in 
error is called rate of the clock. The amount both of 
error and rate can be determined by observing the 

At what time of the year is the equation of time the greatest ? Are the epochs 
when the mean and true solar time agree constant ? AVhy not ? Describe the astro- 
nomical clock. What time does it keep? Explain sidereal time. 



sun's apparent motion in declination. 81 

transits of a star whose position has been accurately 
ascertained, and comparing the clock times with the 
star's right ascension. 

127. Right Ascension — How Determined. The 
observer viewing a star through his transit instrument 
notes by the clock, in the way before stated, the time 
when the star crosses the central wire. This is the 
right ascension, since it measures the star's distance 
from the vernal equinox either in time, or in degrees 
and parts g£ a degree. Thus, if the transit of a star 
occurs when the clock indicates 5 h 50 m 4 s sidereal 
time, its right ascension is 5 h 50 m 4 s , or since 15° cor- 
responds to one sidereal hour, 87° 31'. It this way 
the right ascension of a fixed star, which is a mere 
point, is determined, but to find the right ascension of 
the sun, or of a planet, the times of the transits of the 
opposite edges or limbs must be taken, and the mean 
of these times gives the right ascension of the centre 
of the body. The same method is pursued in finding 
the altitudes of these bodies and of th-3 moon. 



CHAPTER VI. 

OF THE ANNUAL MOTION OF THE EARTH. 

128. Sun's Apparent Motion in Declination. 
If the declination of the sun is measured 1 with an instru- 

1. The declination can be found as follows. In the figure, let Q be the 
place of the observer; HQH 1 the horizon; QNP the direction of the 




north pole of the heavens ; and EQ that of the celestial equator, and S, S l 
two positions of the sun north and south of the equator. Now, the sum 

What is meant by error and rate ? How is the right ascension of a star deter- 
mined ? How is the right ascension of the sun or of a planet determined ? How are 
altitudes determined ? What is the subject of Chapter VI ? If the declination of the 
snn is measured from day to day, what changes are observed throughout the year? 



82 THE EARTH VIEWED ASTRONOMICALLY. 

merit, as the transit instrument, at noon, day after day 
throughout the year, it will be found that in the north- 
ern hemisphere the declination increases from the vernal 
equinox, the 21st of March, to the summer solstice, the 
22d of June, when it amounts to about twenty-three de- 
grees and a half (28 c 27' 37.4"), the sun appearing to de- 
part continually from the equator, towards the north, and 
to rise higher and higher in the heavens. After the 22d 
of June, the declination decreases, the sun appearing 
gradually to move southward, and to approach the 
equator, which it reaches on the 2 2d of September, 
the autumnal equinox, when its declination is nothing ; 
for it will be remembered that declination means dis- 
tance from the equator. After the 22d of September 
the declination increases below the equator, to the south, 
the sun seeming constantly to recede from it, sinking 
lower and lower in the heavens until the 22d of Decem- 
ber, the winter solstice, when its declination amounts 
again, as at the summer solstice, to nearly twenty- three 
degrees and a half. After the winter solstice it again 
begins to move northerly towards the equator, where it 
arrives on the 21st of March, reaching the vernal equi • 
nox after one year from its last departure. 

129. Sun's Apparent Motion in Eight Ascension, 
It is clearly detected by observation that the sun does 
not approach the celestial equator and recede from it in 
a line at right angles to the plane of this circle, but that 
while it is apparently moving to and from the equator, 
it at the same time seems to advance from west to east, 

of the three angles, NQH 1 , NQE, and EQH, is equal to one hundred 
and eighty degrees, because HNPH 1 is a semi-circle ; but NQH 1 is 
known, being equal to the latitude of the place Q, and NQE is a right 
angle, since the equator is ninety degrees from the pole. Subtracting then 
the value of the first two angles from one hundred and eighty degrees, 
and we have that of the angle, EQH, the elevation of the equator above 
the horizon. To find the declination then of the sun, when north of the 
celestial equator, we subtract EQH from the sun's altitude HQS 1 , which 
gives us EQS 1 , which is the declination. -When the sun is south of the 
equator, we subtract the sun's altitude, SQH, from the elevation of the 
equator, which gives EQS , the declination. Corrections, of course, are 
made for refraction and parallax. 

1 What is detected by obterving the sun's apparent motion in the heavens ? 



sun's apparent motion in declination, &c. 83: 

in the order of the signs of the Zodiac. The sun's mo- 
tion in this direction is called its right ascension, and 
can be found, as in the case of the stars, by means of 
the transit instrument and astronomical clock. Under 
the influence, therefore, of these two apparent motions, 
the sun's visible path in the heavens is a curve, which 
is found to be a great circle of the celestial sphere, cut- 
ting the celestial equator at the equinoctial points, at an 
angle which measures about twenty-three degrees and 
a half, (23° 27 / 37.4".) That it is a great circle, is 
proved by tne fact that the points where it cuts the 
equator are one hundred and eighty degrees apart ; for 
the sun, in his apparent path, makes the entire circuit 
of the signs, (three hundred and sixty degrees,) in the 
space of a year, and the distance between the two equi- 
noxes in time is found to be about six months, equal to 
one hundred and eighty degrees of angular measure- 
ment. 

130. Sun's Apparent Path. The sun thjn appar- 
ently moves through the heavens from west k> east, de- 
scribing a vast celestial circle, which cuts the equator in 
the equinoctial points, one circuit being completed in 
the course of a year. But, after all, the sun is sta- 
tionary, and this his apparent motion is the result of 
the actual motion of the earth around the sun. That 
the earth thus really revolves about the sun, will be 
rendered evident in a subsequent chapter, when we shall 
be better prepared to understand and appreciate the 
proofs. To show that such a motion of the earth per- 
fectly explains the apparent motions of the sun, is our 
present task. 

131. Sun's Apparent Motion in Declination Ex- 
plained. In Fig. 30, where the ellipse delineated rep- 
resents the orbit of the earth, the latter is exhibited 
in twelve positions, corresponding to the twelve months. 
In the several globes, N is the north pole, DCL :he equa- 
tor, S l the place of the sun, and CS 1 and all lines from 
parallel to this the direction of the plane of the ecliptic. 

What is meant by the sun's apparent motion in right ascension 1 What kind of a fig- 
ure it described by the sun's apparent path? What is the amount of its inclination to 
the plane of the celestial equator ? How is it proved to be a g-eat circle I What it the 
course of the sun's apparent motion iu 'lie heavens 1 What are we now to show J 



34 THE EARTH VIEWED ASTRONOMICALLY. 

It is sufficient for our present purpose to direct our at- 
tention to the relations between the sun and earth 
in four positions only, viz., at the vernal equinox, (March,) 
the sammer solstice, (June,) the autumnal equinox, (Sep- 
tember,) and the winter solstice, (December.) It is evi- 
dent from the figure, that at the vernal equinox, since 
the plane of the equator passes through the sun, that 
this luminary, viewed from the centre of the earth, 
will be seen in the opposite quarter of the heavens, 
on the celestial equator, at its intersection with the 
ecliptic in Aries. At the summer solstice, the earth 
assumes such a position in respect to the sun, that the 
latter is seen from the earth's centre north of the equa- 
tor, in the line CS 1 , which makes an angle with the 
equator, CD, of about twenty-three and one-half degrees, 
(23° 27' 37.4".) The sun, therefore, appears to have ad- 
vanced north of the equator by this same number of 
degrees. 

When the earth arrives at the autumnal equinox, the 
plane of the equator again passes through the centre of 
the sun, which is seen from the earth, as at the vernal 
equinox, again on the celestial equator at its intersection 
with the ecliptic ; but in the opposite quarter of the 
heavens, in the sign Libra. At the winter solstice, the 
sun is seen in the direction of the line CS 1 , but the 
earth has now so changed its position that this line falls 
south of the equator, making an angle with the latter 
of about twenty-three and one-half degrees, viz., S^L. 
The sun is now seen nearly twenty-three and one-half 
degrees south of the equator. We thus perceive that 
on the supposition that the earth moves while the sun is 
still, the sun appears on the equator at the time of the 
two equinoxes, about twenty-three and one-half de- 
grees to th>3 north of it at the summer solstice, and about 
twenty-three and one-half degrees to the south at the 
winter solstice. Could we follow the changes of the 
position of the earth's equator in respect to the ecliptic 
throughout every day in the year, we should find that 
these changes account satisfactorily for all the variations 

Explain from figure. 



SUN'S APPARENT MOTION IN DECLINATION, &C. 85 




$6 THE EARTH VIEWED ASTRONOMICALLY. 

in the sun's daily declination. The apparent motion 
of the sun in declination is, therefore, the result of the 
earth's actual motion in her orbit. 

132. Sun's Apparent Motion in Right Ascension 
Explained. If a person passes round a tree in any 
direction, the tree, though immoveable, appears to move 
along the distant horizon, following around after him at 
the distance of half a circumference. In the same man- 
ner, the earth being in the sign Libra, the sun appears 
in the opposite quarter of the heavens, at Aries ; and as 
the earth moves round the sun from Libra to Scorpio, 
Sagittarius, &c, the sun also appears to follow round 
in a circle from Aries, through Taurus, Gemini, &c. 
The real motion of the earth in her orbit then accounts 
for the apparent motion of the sun in right ascension, 
from west to east. 

133. The circular motion of the earth around the sun 
thus produces an apparent circular motion of the sun in 
the heavens, and the apparent motion of the sun to and 
from the equator is owing to the fact that the plane of 
the equator is inclined to that of the ecliptic. If they 
coincided, the sun would always appear moving round 
in the plane of the equator. 

134. Direction of Motion in Space Explained. 
A difficulty sometimes arises in the mind respecting the 
direction of motion. The earth rotates on her axis from 
west to east, and yet the people who live immediately 
under us, on the opposite side of the globe, appear to 
move in a contrary direction to what we do. How is 
this to be explained ? We must bear in mind that the 
manner in which the constellations that mark the signs of the 
zodiac succeed each other determines the direction of circular 
celestial motion. At night we see these constellations 
rising above the horizon in the following order, viz., 
Aries, Taurus, Gemini, &c, and when owing to the rota- 
tion of the earth they rise above the horizon of China, 
they will succeed each other in the same order, and every 

Explain why the real orbitual motion of the earth produces an apparent motion of the 
tun in right ascension. What is the sun's apparent motion in declination owing to? 
What is understood when we say that a heavenly body rotates, or revolves,, from w*st u> 
•ast? 



LENGTH OF THE YEAR, HOW FOUND. 87 

observer upon the earth beholds them rising in this 
manner. These constellations recurring in this order, 
the eartih is said to revolve from west to east. If they 
succeeded each other in a contrary order, for example 
Gemini, Taurus, Aries, &c., the earth would revolve 
from east to west. 

We thus see why the sun and the earth, though ap- 
pearing to move in opposite directions on the great 
circle of the ecliptic, are yet really moving in the same 
direction, since they pass through the signs in the same 
order ; the sun apparently passing through them ; the 
earth actually. 



CHAPTER VII. 



OF THE YEAR. 



135. The length of time employed by the earth in per- 
forming an entire circuit from any point in the ecliptic, as 
the summer solstice, to the same point again constitutes 
a tropical 1 year, which contains three hundred and 
sixty-five days, five hours, forty-eight minutes, and forty 
seven eight-tenths seconds (365d. 5h. 48m. 47.8sec.) The 
fractions of a day belonging to a year of this length 
would be manifestly inconvenient for the purposes of 
society, and for this reason the civil year is made to 
consist of three hundred and sixty -five entire days. 

136. Length — how found. The simplest method 
of ascertaining the approximate length of the year, and 
one which was employed by the ancient astronomers, 
consists in erecting a vertical rod of unchanging length, 

1 . Tropical year so called, from the Greek word trepo, to turn because 
the sun reverses its apparent course upon arriving at either solstice. 
In our summer, after advancing apparently as far north as the summer sols 
tice, it then turns back to the south, and in winter, after retreating as far 
south as the winter solstice, it turns back to the north. 



What it the subject of Chapter VII. 7 How is the length of a tropical year measured 7 
What is its length 7 What is the length of a civil year ? Why is not the tropical year 
employed as the civil year 1 What is the easiest method of ascertaining the length ot 
the year 7 



88 THE EARTH VIEWED ASTRONOMICALLY. 

on a smooth horizontal plane, upon which plane a merid- 
ian line is drawn, and the length of the shadow of the 
rod marked on the plane every day at noon throughout 
ths year. When the sun rides highest in the heavens 
on the day of the summer solstice, the shadow will then 
be the shortest, and the number of days elapsing between 
two successive returns of the shortest shadow, will be 
the approximate length of a tropical year. 

137. The length of the tropical year was thus at a 
very early period discovered to be about three hundred 
and sixty-five days. But the difference of nearly six 
hours which existed between this period and the true 
length of the year, was soon detected, and its duration 
was then fixed at three hundred and sixty -five and one- 
fourth days ; the dates of the year were thus made for a 
time to correspond nearer with the points in the earth's 
orbit, which they are intended to indicate. 

138. A celebrated ancient astronomer, Hipparchus of 
Alexandria, in Egypt, who flourished one hundred and 
forty years before the Christian era, discovered however, 
that this estimation of the length of the year was not 
correct. Instead of making his observations at the sols- 
tice, when the earth moves so nearly parallel to the plane 
of the equator, that the shadow of the rod shortens for 
some days, by almost imperceptible degrees, he made 
them at the equinoxes ; when the length of the shadow 
changes most rapidly, since the path of the earth in its 
orbit is then most inclined to the equator. By pursuing 
this method he found that the actual length of the year 
was less than the computed by a quantity which he 
estimated at 4m. 48sec. The duration of the year thus 
corrected was now three hundred and sixty-five days, 
iive hours, fifty -five minutes, and twelve seconds, (365d. 
5h. 55m. 12sec.) 

From the era of Hipparchus to the present time, vari- 
ous corrections have been made in the length of the year ; 
for within this period the true laws of the universe have 
been revealed, and astronomers, furnished with instru- 

Whnt was the length of the tropical year according to the earliest known observations ? 
What further discovery was soon made 1 Was the true length of the year now obtained 1 
Who discovered the error? What method of observation did he pursue, and why f 
What results did he obtain ? 



THE CALENDAR. 8£ 

meats of surprising accuracy, and aided by new and won- 
drous mathematical agencies, have attained a precision 
of calculation almost beyond belief. Yet in the subject 
before us, the ancient computations have passed through 
this severe ordeal, almost untouched, for the closest ap- 
proximation to the true length of the year for 1800, as 
computed by Bessel is three hundred and sixty-five 
days, five hours, forty-eight mintites, and forty-seven 
eight-tenths seconds, (365d. 5h. 48m. 47.8sec.) a result 
which differs from that of Hipparchus by less than seven 
minutes. 

139. The Calendar 1 . In order to avoid fractions in 
reckoning the length of the year, it has been the custom 
of all nations who have made any progress in the art of 
computing time to regard the civil year as consisting of 
an even number of days — making however, at stated 
intervals, such corrections, that the real position of the 
earth in its orbit shall on the whole correspond with the 
position indicated by any date in the year ; so that the 
seasons shall always occur in the same months, and the 
solstices and equinoxes return at the same time in their 
respective months. A moments reflection will show 
the necessity of such corrections. Four civil years are 
shorter than four tropical years by nearly one day, 
(4 x 5h. 48m. 47.8s) so that in every four years about 
one day would be lost in the reckoning. For if the 
reckoning commenced at the day of the summer solstice 
on the 22d of June ; four years afterwards on the 22d of 
June, the earth would not have arrived at the solstice 
by a day's journey, and the solstice would take place on 
the 23d. In four years more it would happen on the 
24th, and in four more on the 25th, and so on. This 
mode of reckoning if continued uncorrected would thus 
in course of time make either solstice, or any other po- 
sition of the earth in its orbit, occur successively on every 
day of the civil year. 

1. Calendar, i. e., a register of the year from the Latin, ealendarium. 

Compare the ancient computations with the modern 1 What has been the custom ol 
ell nations who have possessed a knowledge of the computation of time, in regard to tb* 
civil year 1 Supposing the year to consist of three hundred and sixty-five days only 
whet would happen if no corrections were made ? 



9p THE EARTH VIEWED ASTRONOMICALLY. 

140. Sothic Period. The ancient Egyptians were 
aware of this, and purposely suffered their public festi • 
vals, though recurring at the same date, to run through 
the entire natural year. " They do not wish," says Ge- 
minus, " the same sacrifices of the gods to be made per- 
petually at the same time of the year, but that they 
should go through all seasons, so that the same feast 
may happen in summer and winter, in spring and 
autumn." The period in which any festival would pass 
through an entire civil year of the length of three hun- 
dred and sixty -five and one-fourth days is one thousand 
four hundred and sixty years of the same duration, 
(1,460,) since one thousand four hundred and sixty years, 
each consisting of three hundred and sixty-five and one 
fourth days, are equal to one thousand four hundred and 
sixty-one years, the duration of each being reckoned at 
three hundred and sixty-five days. This period of one 
thousand four hundred and sixty years, at the end of 
which either the solstice or any other given position of 
the earth would happen on the same date again, after 
falling upon every day of all the months of the year, 
was called by the Egyptians the Sothic x period; because 
it began on the first day of that year when the dog star 
rose with the sun. The length of the tropical year was 
computed by the early Egyptians to be three hundred 
and sixty -five and one-fourth days. 

141. Mexicans. The Mexicans regarded the year as 
consisting of three hundred and sixty-five days, but 
made a correction of thirteen days for one period of 
fifty-two years, and twelve for the next, amounting to a 
correction of twenty-five days for every one hundred 
and four years. The accuracy obtained by this method 
is truly surprising for the excess of the actual over the 
civil year; viz., five hours forty-eight minutes and 

1. Sothis in the Egyptian language, means the dog-star, which astrono 
»ners call Sirius. 



What was the custom of the ancient Egyptians ? Why did they adopt this custom 
In what period of time would any date or festival pass througn one entire civil year hav- 
ing a length of three hundred and sixty-five one-fourth days ? Explain why. What 
name was given to this period., and why"? What was the length of the tropical year at 
computed by the early Egyptians "? What as computed by the Mexicans 1 What is said 
of the accuracy of their correction ? 



MEXICANS. 91 

torty-feven eight-tenths seconds, multiplied by one hun- 
dred and four, gives as a product twenty-Jive days four hours 
thirty-four minutes and fifty-one seconds, the error of reck- 
oning in a century being only about four and a half hours. 

142. The Christian Calendar — Julian Correction. 
This is derived from the Romans. The civil year is here 
made to consist of three hundred and sixty-five days, 
the necessary corrections, or intercalations 1 as they are 
termed, being applied at stated intervals. The first 
correction in this calendar was made by Julius Caesar 
forty-five years before the Christian era. At this time 
the Roman calendar had fallen into such disorder that 
ninety days were obliged to be added to the previous 
year, making it four hundred and fifty-live days long 
so as to bring the position of the earth in its orbit to 
correspond with the date of the civil year-, by this 
means the error in reckoning which had been accumu- 
lating for centuries was destroyed. In order to pre- 
vent any future derangement, the rule was adopted of 
adding one day to every fourth year, by giving Febru- 
ary twenty-nine instead of twenty-eight days. This 
fourth year is called the Bissextile ' or leap-year. 

143. Gregorian Correction. But the Julian cor- 
rection was too great, because the year was thereby 
assumed to be three hundred and sixty-five days and 
six hours long, when in fact it is about eleven min- 
utes shorter (11 minutes 12.2 seconds,) an error which 
in the course of nine hundred years would amount 
to very nearly seven days. This small annual error 
did not at once produce any material derangement in 
the calendar, but in the year 1414, A. P., it was per- 
ceived that the vernal equinox which should always 
have happened on the 21st of March, if the Julian cor- 

1. Intercalation, means the insertion of a day in the calendar, from the 
Latin intercalatio, the putting a day between two others. 

2. This year was called the year of confusion. 

3. Bissextile, because in this year the sixth day before the first of Man h 
was reckoned twice. Latin bis twice, sextus sixth. Hence Bissextile. 



Whence is the calendar in use among Christian nations derived ? What is the length 
ot the civil year, and how are the corrections made 1 By whom was the first correction 
of the calendar made ? When ? Whv particularly nt this time ? How was it made, 
and what rule adopted ? Why is the leap-year called Bissextile? Was the Julian cor 
(rect ion rxact ? Why not ? How great an error would arise in nine hundred veurs ' 



92 THE EARTH VIEWED ASTRONOMICALLY. 

rection was perfectly exact, was gradually occurring 
earlier. In the year 1582, the error had amounted to 
about ten days, and a reform was made by Pope Gregory 
XIII. It was well known to astronomers that in the 
year 325 A. D., the equinox fell upon the 21st of 
March according to the civil reckoning, but in the year 

1582, it occurred on the 11th of the same month, the 
various positions of the earth in its orbit were thus in 
advance of the dates which should have indicated these 
positions by ten days. The remedy was obvious and 
consisted in omitting ten nominal days, calling the day 
next succeeding the 4th of October the 15th, instead of 
the 5th. This change was made at once in all Catholic 
countries, but was not adopted in England until the 
year 1752, by which time the error had amounted to 
eleven days. The change of style, as it is termed, was 
there effected by an Act of Parliament, decreeing that 
the day after the 2d of September, old st}de, should be 
called the 14th, which was the first day of the new style ; 
and by the same authority the year which before had 
begun on the 25th of March, was made to begin on the 
1st of January. This latter change was accomplished 
by making the preceding year (1751,) to consist of nine 
months only, causing it to end at the beginning of the 
1st of January instead of the 25th of March. The yeai 
1752 commenced on the 1st of January. 

144. By the omission of ten days, Pope Gregory thus 
reformed the calendar, so that on any day of the year 

1583, the earth occupied substantially the same place in 
its orbit as it did on the same day in the year 325 A.D. 
But this correspondence was only temporary for the same 
error of 11m. in the reckoning would work the same 
mischief in course of time, as it had already done, 
if let alone ; to prevent therefore any future discordance 
in the calendar, the following rule was adopted under 
the sanction of the same pontiff. 

How much did the error amount in the year 1582? By whom was a reform made? 
How was the amount of error ascertained ? How was it corrected ? Where was the 
change at once adopted ? When introduced into England ? What was the amount of 
error then? How was the change of style effected, and what alterations were made in 
the calendar ? How wus the second change accomplished ? Was the first correction rf 
Pone Gregory all that was necessary to render the calendar perfectly accurate ? Why not ' 



THE PRECESSION OF THE EQUINOXES. 93 

145. Gregorian Eule. Every year whose number in 
not exactly divisible by four consists of three hundred and 
sixty-five days. Every year which is so divisible, but not 
divisible by one hundred, of three hundred and sixty-six 
days. Every year whose number is divisible by one hun- 
dred but not by four hundred, contains three hundred and 
sixty-five days ; and every year whose number %s divisible by 
four hundred of three hundred and sixty -six days. Thus, 
for example, the year 1851, consists of three hundred 
and sixty -five days, because the number 1851, is not ex- 
actly divisible by four, while 1852 consists of three hun- 
dred and sixty-six days, because the number 1852 is 
thus divisible. The years 1700 and 1800, have each 
three hundred and sixty -five days, because these num- 
bers are exactly divisible by one hundred, but not by 
four hundred; while the years 1600 and 2000, are leap- 
years, since four hundred divides these numbers with- 
out a remainder. By the adoption of this rule the civil 
and tropical years are made to correspond so nearly, 
that an error of only about twenty-two hours, (22h. 
39m. 20sec.,) occurs in the space of four thousand years. 



CHAPTER VIII. 

OF THE PRECESSION OF THE EQUINOXES, CHANGE OF THE POLE STAR, 
AND NUTATION. 

146. Of the Precession of the Equinoxes. The 
determination of the exact position of the vernal equinox 
(which is the place in the heavens where the sun appa- 
rently crosses the equator in the spring,) is a matter of 
great importance, since it is the point 1 from whence right 
ascension is reckoned. Eepeated observations taken at 

1. The scholar must remember that this point is imaginary , it is one of 
the two points, were two imaginary circles, the equator and ecliptic cut 
each other. 

Give the Gregorian Rule ? What is said respecting the correspondence of the ci'il and 
tropical year when the rule is employed ? What does Chapter VIII. treat of? Why 
is the determination of the place of the vernal equinox a matter of importance? vVhal 
phenomenon has been detected, and how ? 



94 THE EARTH VIEWED ASTRONOMICALLY. 

considerable intervals of time have detected a remarka« 
ble phenomenon in regard to this point ; namely, that it 
is not stationary in the heavens. For if on any given 
year the position of the equinox in the heavens is found 
to be in a line with any fixed star, on the next year it 
will be seen to the west of the star, and in succeeding 
years the equinoctial point will fall farther and farther 
to the west of the same luminary. The annual amount 
of this angular motion is only fifty and one-fourth 
seconds in longitude, (50\") and as this quantity is con • 
tained twenty-five thousand, seven hundred and ninety ■ 
one times (25,791,) in one million two hundred and 
ninety-six thousand seconds, (1,296,000") 1 or an entire 
circumference, it takes twenty-five thousand seven hun- 
dred and ninety-one years for the equinoctial points to 
make one complete circuit of the ecliptic. 

147. We may form an idea of the way in which this 
phenomenon occurs by imagining the' axis of the celestial 
equator to revolve about that of the ecliptic from east to 
west once every 25,791 years, the axes always pre- 
serving nearly the same distance from each other. Since 
the axes are perpendicular to their respective planes, the 
planes through their entire revolution will preserve their 
original inclination to each other, and while the pole of 
the celestial equator revolves around the pole of the 
ecliptic, the line joining the equinoxes (which is the line 
of the intersection of the two planes,) will also move 
round in the plane of the ecliptic from east to west. 
Thus, in Figure 31, if E'FQ represents the plane of the 
celestial equator and EFC that of the ecliptic, P*B the 
axis of the equator, PB that of the ecliptic, and DF the 
line of the equinoxes ; it is evident that if the pole of the 
equator P l , revolves in a circle L about the pole of 
the ecliptic P from east to west two things will occur. 
First, that the equinoctial points D and F will move 

1 . 360O x 60 X 60 = 1 ,296,000". 

2. It will be remembered that the axis of a great circle like the equatoi 
is the straight line that passes through its centre perpendicular to its 
plane. 

What is the annual motion of this point in longitude 1 In how many years would it 
make the circuit of the ecliptic t In what way can we form an idea of this motion of th» 
•nuinoctuJ points 1 Explain from figure. 



THE PRECESSION OF THE EQUINOXES. 



95 



round in the same directum. Secondly, that the planes 
of the equator and ecliptic will maintain the same inclir 
nation, to each other throughout the entire revolution since 




PRECESSION EXPLAINED. 



P 1 is always at the same distance from P revolving as it 
does in a circle about P. 

148. The following illustration may tend still further 



FIG. 32 




PRECESSION EXPLAINED. 



to elucidate this subject. Take a tumbler DC, Fig. 32, 
partly filled with water. The level surface of the water, 

Illustrate the subject still further by the aid of Fig. 32 

5 



96 THE EARTH VIEWED ASTRONOMICALLY. 

EF, we will call the plane of the ecliptic, and the end A 
of a thread SA, which hangs over the middle of the 
tumbler the pole of the ecliptic. Now procure a circle 
of stiff pasteboard (n), a little smaller than the inside of 
the tumbler, and through its centre thrust a wire (W,) fill- 
ing it perpendicularly to the surface. The plane of the 
pasteboard represents the plane of the equator, and the 
wire its axis. Taking now the pasteboard by the wire 
we place it in the tumbler, causing half the circle to sink 
below the surface of the water, and half (h,) to rise 
above, making an angle with the surface of the water 
EF of about twenty-three and one half degrees. The 
plane of the pasteboard then represents that of the equa- 
tor, the surface of the water the plane of the ecliptic, 
the line where the pasteboard meets the water ; viz., g ) 
the line of the equinoxes, and around the tumbler at the 
water-line the signs of the zodiac may be supposed to 
be arranged, thirty degrees apart. Causing now the 
up^>er end of the wire, B, (the pole of the v equator) to 
describe the circumference of a circle around the lower 
end of the thread, A, (the pole of the ecliptic) from east 
to west, we shall see tha/t the line where the pasteboard 
meets the water, that is, the line of the equinoxes, moves 
also around from east to west ; and that the equinoxes 
which are the extremities of this line, change their posi- 
tion in the same direction. 

149. Sidereal Year. A sidereal year is the time 
taken by the earth to perform one entire revolution in its 
orbit, and is determined by noting the period that elapses 
during its passage from a fixed star round to the same 
star again. Hence its name, from the Latin word sidera, 
meaning stars. 

150. In consequence of the precession of the equinoxes 
the earth does not peiform an entire revolution about 
the sun, in the course of a tropical year, which it will 
be remembered is the time that elapses between the de- 
parture of the sun from one of the equinoxes to its 
next return to the same point. 

151. Now when the earth leaves the vernal equinox, 

Wftnt i'« mennt by the term sidereal year 1 How is it determined 1 Why so called 1 
Why does it differ in length from the tropical year 7 



OHAJSGE OF THE POLE STAR. 97 

moving in the direction from west to east, the next ver- 
nal equinox occurs when the earth lacks fifty and one- 
fourth seconds 1 of angular motion of completing its revo- 
lution around the sun. The time the earth takes to 
pass through an arc of fifty and one-fourth seconds, is 
twenty minutes, and twenty-two nine-tenths seconds of 
mean solar time, which must be added to the length of the 
tropical year to make a sidereal year. The length of the 
tropical year is 365d. 5h. 48m. 47.8sec., adding to this 
20m. 22.9sec. we have, 365d. 6h. 9m. lO.Tsec. for the 
length of the sidereal year. 

153. Change of the Pole Star. Another result 
of the precession of the equinoxes is the curious fact that 
the axis of the earth is not always directed to the same 
points in the heavens, and since the axis of the earth pro- 
longed to meet the starry vault, becomes the axis of the 
heavens, the poles of the celestial sphere are not stationary 
in the sky. Conceiving the pole of the equator to 
revolve slowly around the pole of the ecliptic in the 
manner already explained, it is evident that while the 
former approaches some stars it must recede from 
others. That star which is nearest to the pole of the 
equator is always termed the pole star. 

154. The present pole star (which is in the constella- 
tion 2 of the Lesser Bear, at the end of the tail,) though 
now only one degree and a half from the pole, was at 
the time of the construction of the earliest star maps, 
twelve degrees distant from it. The north pole of the 
heavens will continue to approach this star until it 
is within half a degree, when it will begin to recede, and 
in the course of twelve thousand years, the brightest star 
in the constellation of the I /re will become the pole star. 
For although this luminary is now more than fifty-one 
degrees (51° 20' 49") disiant from the pole, it will then 

1 More nearly 50.24." 

2 Constellation, a cluster of fixed stars. The stars have all been 
' grouped into constellations by astronomers. 

What it the amount of this difference 7 What is the length of the sidereal year 7 An 
the poles of the heaven stationary 7 Why not 7 What is meant by the term pole star ? 
State what is said respecting the present pole star 7 What changes will oceur in regard to 
the pole star in the course of twelve thousand years 7 Is the pole star always the sam8 
orb 7 



98 THE EARTH VIEWED ASTRONOMICALLY. 

be within the distance of five degrees. The pole star 
is not therefore forever and unchangeably the same 
luminary. 

155. Effect of Precession on the Eight Ascen- 
sion and Longitude of the Stars. Since the vernal 
equinox is the point from whence the position of the stars 
is determined both in respect to longitude and right as- 
cension, the backward motion of the equinoxes necessa- 
rily produces a slow change in the amount of these 
measurements though the relative positions of the stars 
remain unaltered. Just as the several distances of <ill 
the trees in a grove, from a boat slowly floating down 
a neighboring river, are continually changing, since the 
point from whence these distances are reckoned is con- 
stantly moving, while the distances of the trees from one 
another remain fixed. 

156. On their Declination and Latitude. On 
account of the precession the declination also of the stars 
does not remain constant; for since the axis of the equa- 
tor, as it moves around that of the ecliptic, is always at 
right angles to the plane of the equator, this plane has 
necessarily a corresponding motion among the stars. 
From century to century the distances of the fixed stars 
from the celestial equator must therefore vary, and 
these distances are their declinations. The latitude of 
the stars experiences no change from this cause, since the 
precession produce no variation in the position of the 
ecliptic from which the latitudes are reckoned. 

157. Terrestrial Latitude Constant. Terrestrial 
latitudes are unaffected by the precession of the equi- 
noxes, which shows that the change in the position of 
the earth's axis in space, is not a mere shifting of the 
line about which the earth re tates ; for if this was so the 
geographical situation of places in respect to the poles, 
or what is in effect the same their latitudes, would also 
change, which is not the case. The earth therefore 
rotates about an axis invariably the same, and in the motion 
of this axis around that of the ecliptic, " the entire body 

State what is said respecting the effect of precession on the right ascension and longi- 
tude of the stars 1 What on their declination and latitude ? Does the precession affect 
terrestrial latitudes ? What does this fact show? What is said respecting thecarth'i 
axis ? 



&c. 99 

of the globe participates," says Herschel, "and goes 
along with it as if this imaginary line were really a bar 
of iron driven through it. This is not only proved by 
the unchangeability of the latitudes, but also by the fact 
that the sea maintains invariably its own level which 
would not be the case if the axis of rotation changed." 

158. Kelative positions of the Signs and Con- 
stellations of the Zodiac Variable. On account 
of the precession of the equinoxes the signs of the Zodiac 
do not now correspond with their respective constellations, 
but have retrograded through the heavens the space of 
one sign or thirty degrees. 

159. When the vernal equinox occurs the sun is at 
the first point in the sign Aries, in the Zodiac, but at this 
time he is seen from the earth, not in the constellation 
Aries, but in that of Pisces thirty degrees distant from 
the first point in the sign. The same change has taken 
place in all the signs, each has moved backwards thirty de- 
grees, so that the sign Aries is now in the constellation 
of Pisces, the sign Taurus in the constellation Aries and so 
on throughout the entire Zodiac. 

160. When the first catalogues of stars were con- 
structed the signs doubtless corresponded with their con 
stellations in position, and we can therefore calculate the 
era when the earliest star charts were made. Thus the 
rate of precession for one year, (50. 24") is to one year as 
thirty degrees (108000") is to 2149.7 years. The Zodiac 
was therefore constructed about two thousand years ago. 

It is important to discriminate clearly between the 
signs of the Zodiac and the constellations. The constella- 
tions of the Zodiac are groups of fixed stars in the plane of 
the ecliptic unchanged in position by the precession. The 
signs of the Zodiac are twelve equal divisions of the great 
circle of the ecliptic, bearing the same names as the con- 
stellations. They are reckoned from the vernal equinox 
beginning with Aries, forward through Taurus, Gemini, 
and so on. The backward motion of the vernal equinox 

What does Herschel observe! What additional proof of the constancy of the earth's 
axis is adduced 1 State what is said respecting the want of correspondence between the 
signs and constellations of the Zodiac ? When did the signs and constellations of the 
Zod inc. correspond in position? Prove it. Explain the terms constellations and sign* 
tf Vis Zodiac 7 How are the latter re:koned/oricartZ ? 



100 THE EARTH VIEWED ASTRONOMICALLY. 

carries back all the signs at the same rate through the 
fixed series of constellations. In about twenty -four thou- 
sand years from the present time, the signs will again 
correspond with their constellations. 

CAUSE OF THE PRECESSION. 

161. We have seen in our investigation of the figure 
of the earth that there exists an excess of matter around 
the equator ; the equatorial diameter being twenty-six 
miles longer than the polar. A ring of solid matter 
thirteen miles in thickness, therefore, surrounds the earth 
at the equator above what is necessary for forming a 
perfect globe, having an equatorial diameter equal in 
length to the polar diameter. Now it is the action of 
the sun, moon, and planets upon this ring which pro- 
duces such a displacement in the position of the equa- 
tor, in regard to the ecliptic as gives rise to the preces- 
sion of the equinoxes. 

162. Influence of the Sun. The action of the sun 
is as follows. This vast globe being in the plane of the 
ecliptic, to which the plane of the ring is inclined about 
twenty-three and one half degrees, ' tends by its attrac- 
tive force to draw down the ring to the plane of the 
ecliptic, while at the same time the earth, and of course 
the ring, is revolving on its axis from west to east. 

163. The effective force of the sun acts at right angles 
to the plane of the equator and the force of the rotation in 
the plane of the equator from west to east. The rotating 
ring of matter is therefore acted upon at the same time 
by two forces, one of which causes it to rotate from west 
to east, and the other to draw it down to the plane of the 
ecliptic. By their joint action, the ring really moves as 
if drawn by one force acting obliquely to its plane, and is 
as it were twisted round from east to west, intersecting 

1 . The plane of the ring is that of the equator, and its inclination to 
the plane of the ecliptic will be the same ; viz., 23° 27 / Z&JS", or about 
23£. 

How long will it be before the signs and constellations correspond in position "? What it 
the cause of the precession of the equinoxes ? Explain the action of the sun? What 
two forces combine to produce the precession 1 What :s the effect of their joint action ' 



NUTATION. 101 

the ecliptic at points westward of those were it cut it 
before. 

164 The ring is moved in the same manner as a boat 
which sails directly across a river from west to east, 
w Kile at the same time it is slowly drawn down the 
stream by the current. By the union of both these 
lorces it descends the river as if influenced by a single 
force acting obliquely to the keel. Every one will of 
course understand that the ring in its motions carries 
the earth along with it. 

165. Influence of the Moon and Planets. The 
moon's influence in causing the precession of the equi- 
noxes, is greater than that of the sun, on account of 
its being nearer to the earth, being as seven to three , 
and their united effect produces a displacement of the 
equinoxes from east to west. The attraction of the 
planets is, however, exerted in an opposite direction, 
causing a very small advance pf the equinoxes from 
west to east. The actual precession is the first motion 
diminished by the latter. The result obtained is that 
already stated, namely, 50.24". 

NUTATION. 

166. We have stated that the precession of the 
equinoxes is caused by the attraction of the sun, 
moon, and planets, upon the excess of matter at the 
earth's equator, and that in consequence of this ac- 
tion the pole of the equator describes the circumference 
of a circle around the pole of the ecliptic in about 
twenty -six thousand years. If this action of the sun 
and moon was always the same, the path of the pole of 
the equator would be a circle ; but this is not the case, 
for the force of the sun varies — its influence being greatest 
upon the equatorial ring, when it is farthest from the 
earitis equator, namely, at the solstices, and hast, vanish- 

1. Nutation, from the Latin word nutatio, a nodding, a moving from 
one side to the other. 

Give the illustration. State what it said respecting the influence of the moon awl 
pJineU. Explain nutation. Solar. 



102 THE EARTH VIEWED ASTRONOMICALLY. 

ing to nothing, when it is at the equator, namely, at the 
time of the equinoxes. 

168. A similar inequality likewise exists in the moon's 
action, arising from a like cause. There is, however, 
this difference. The variations in the solar force all 
occur in the space of one year, those of the lunar within 
the period of about eighteen and a half years. 

169. This variation of force produces the nutation, 
and the pole of the equator, if free from any other in- 
fluence, would, in virtue of this, describe among the 
stars a small ellipse in a period comprising about eighteen 
and a half years ; the longer axis of the ellipse being 
about 18-".5, and the shorter, 13". 7. The centre of the 
ellipse lies in the circumference of the circle which would 
be described by the pole of the equator round the pole 
of the ecliptic, if the force producing the precession 
never varied. 

170. This subject is illustrated in Fig. 33, where the 

FIG. 33/ 




circumference, B, of the large circle, represents the patb 
that the pole of the equator, P 1 would describe around 
the pole of the ecliptic, P, if precession alone existed ; and 
A, is the small ellipse which P 1 would describe if nutation 

Lunar. Within what period of time do the solar variations occur? Within who'* 
the lunar? What kind of figure does the pole of the equator describe in consequence 
of nutation? What is the extent of this ellipse ? Where does its centre lie ? Illustrate 
this subjeet by figures 33 and 34. 



NUTATION. 108 

occurred without precession. Now, since these motions 
co-exist, it is evident that neither a perfect circle nor a 
complete ellipse will be described by the pole, P 1 ; but 
at one time it will be outside the circumference, B, and 
at another within, revolving about P all the while. It 
will, therefore, actually describe a circular waving path, 
like that exhibited in Fig. 34, where P is the pole of the 
ecliptic, and the pole of the equator advances towards 
P and recedes from it, as it follows the path, AA l BB l , 
and so on. 




171. The influence of the moon in producing nuta- 
tion is to that of the sun, as five to seven. 

172. Obliquity of the Ecliptic Affected by Nu- 
tation. It is evident from an inspection of the above 
figure that the pole of the equator approaches to and re- 
cedes from the pole of the ecliptic at determinate in- 
tervals of time. The inclination of the plane of the 
equator to that of the ecliptic must, therefore, fluctuate 
in the same manner, since the axes of the equator and 
ecliptic are always at right angles to their respective 
planes. A variation, termed secular, also exists, extend- 
ing through centuries, as is shown by the following 
table : 

What is the ratio of the moon's influence to the sun's in producing nutation ? Is the 
•bliqnity of the ecliptic effected by nutation 1 Why? Do recorded observations alM 
•how a ttcniar change in the obliquity ? Prove this from the table given 
5* 



104 THE EARTH VIEWED ASTRONOMICALLY. 

13»te. Obierren. Obliquity. 

1100 Tcheou-kong, (Chinese,) 23° 54' 02" 
324 Pytheas, of Marseilles, 23° 49' 20" 
140 Hipparchus, 23° 51' 15" 

830 Almamun, 23° 33' 52" 

879 Albategnius, 23° 35' 00" 

1690 Flamsteed, 23° 28' 56 

1825 Bessel, 23° 27' 43,4' 

173. The change in the situation of the pole of the 
equator arising from nutation will likewise cause a slight 
periodical variation in the right ascensions, declinations, 
and longitudes of the fixed stars. 






CHAPTER IX. 

OF THE EARTH'S ORBIT. 



174. The path described by the earth in its revolution 
about the sun is an ellipse ; this is proved by observa- 
tion in two ways. First, by the changes in the apparent 
diameter of the sun. Secondly, by variations in its ap- 
parent velocity. The following illustration will enable us 
to understand why these changes lead to a knowledge 
of the true form of the earth's orbit. 

175. Suppose that above the centre of a large circular 
field, an immense gilt globe was fixed in an elevated 
position, and that a person drove around the field always 
preserving the same pace, and keeping at the same dis- 
tance from the globe. Under these circumstances (if he 
were unconscious of his own motion) the globe would 
appear to move around him with the same unvarying 
motion, and to be always of the same size. But if the 
field was elliptical in shape, and the globe above one of 
the foci, and the experimenter drove most rapidly when 

What other variations does nutation cause 1 What is the subject of Chapter IX ? 
What is the figure of the path described by the earth around the sun ? In what two 
ways is this proved 1 Give the illustration. 



SUN'S APPARENT DIAMETER. L05 

»~ rest the globe, and slowest when most remote from it, 
he would, (being unconscious of his own motion, as be- 
fore,) behold the globe changing its apparent size and 
rate of motion as it performed its seeming circuit around 
him ; possessing the greatest apparent size and swiftest ve- 
locity when nearest, and appearing the smallest and moving 
the slowest when most distant. 

176. It is in this manner that we view the solar orb. 
Our globe is the car on which we ride, and we sweep 
through space around the sun at differing distances from 
it, and with changing speed ; but all unconscious of oui 
own motion, the sun seems to move around us, varying 
its velocity and apparent size. These changes in respect 
to the sun show that it is not in the centre of the figure 
that the earth describes around it. The true figure of 
t; e orbit is found in the following way. 

177. Apparent Diameter. If the apparent diameter 
of the sun is taken at stated intervals as at noon through- 
out the year, and his apparent daily angular motion in 
tht ecliptic is likewise observed, we have the means of 
solving this problem. It is a law in optics, that the ap- 
parent magnitude of a body is inversely proportioned to 
its distance ; l that is if at a certain distance it appears of 
a ceitain size, when ten times nearer it will appear ten 
times larger, and if five times farther off five times smaller, 
and so on. 



1. This law is easily understood by the aid of the annexed cut, where the 
same body, represented by the circle A, is placed at different distances 




from the eye at C. At the distance CB 1 the body A is seen under the 
angle DCL 1 which is 10°. Ten degrees is at this distance its apparent 
diameter. At the distance CB which is twice CB 1 the apparent diameter 
of A is LCD, the half of DCL 1 or an angle of Jive degrees. Thus the law 
is proved. 



Apply it to the motions of the earth in reference to the sun 1 What do the change* 
mentioned show in respect to the position of the sun 7 



106 THE EARTH VIEWED ASTRONOMICALLY. 

178. Bearing this law in mind, and having all the 
above observations, we take upon a card a point E, Fig. 
35, which we call the earth and another S, the sun, and 




VARTH'S ORBIT, 



draw a line SE one inch in length for instance* repre- 
senting the distance of the sun from the earth on the 
day when the sun appears the largest. We now draw 
for the next day a line ES 1 making an angle with ES 
equal to the observed angular motion of the sun, since 
it was at S the day before ; and we determine the length 
^f the line ES 1 by making it as much longer than SE, 
ds the apparent diameter of the sun when at S 1 is less 
than when at S. For the next day we proceed in the 
same manner, and so on for the entire year, fixing the 
distances of the lines ES, ES, 1 ES, 2 &c, from each other 
by means of the apparent daily motion of the sun, and 
determining the length of these lines hj the variations in 
its apparent diameter. Then joining the ends of these 
lines we have a figure that represents the orbit of the 
earth. 

179. The figure thus approximately formed is similar 
to an ellipse, and which by rigorous and refined calcula- 
tions is proved to be an exact ellipse. We must recol- 

State the manner in which the true orbit is approximately found ? What has beea 
•roved by rigoroui mathematical calculations ? What must we recollect 1 



ANOMALISTIC YEAR. 107 

lect however, that since it is the sun which is stationary, 
and the earth that moves, the true place of the sun in the 
figure is at E, one of the foci of the ellipse, while the 
earth moves round in the curve occupying the positions 
S, S\ S 2 , S 3 , &c. 

180. The apparent diameter of the sun which is its 
angular breadth, can be measured by various instru- 
ments, but one called a heliometer, 1 is constructed par- 
ticularly for this purpose. When the earth is farthest 
from the sun, the apparent magnitude Of the latter is 
31 / 31" and when nearest 32' 35". 

181. That point in the orbit of the earth, or in that 
of any planet or comet, which is nearest to the sun is 
called its perihelion* and that which is most remote its 
aphelion, 3 the former term signifying about the sun and 
the latter meaning from the sun. 

In the case of the earth its perihelion is also called the 
perigee* and its aphelion the apogee. 5 These terms are 
used in reference to the apparent approach and recession 
of the sun from the earth. 

The perihelion and aphelion, have also the name of 
apsides, 6 and the line which joins them is termed the line 
of the apsides. 

182. Anomalistic year. The places of the perihe- 
lion and aphelion are not fixed as regards absolute space 
but have a gradual motion from west to east. 

183. If we were to note this year the exact time when 
the sun had the greatest apparent diameter, at which mo- 
ment the earth of course would be at its perihelion, and 
determine at this instant the position of the earth in 
reference to the fixed stars, on making the same obser- 

1. Heliometer, from the Greek hclios the sun, and metron a measure 
I. e., a sun-measurer. 

2. Perihelion, from the Greek peri, about, and helios the sun. 

3. Aphelion, from the Greek apo, from, and helios the sun. 

4. Perigee, from the Greek peri, about, and ge, the earth. 

5. Apogee, from the Greek apo, from, and ge, the earth. 

fc. Apsides, from the Greek apsis, meaning a binding together. Any 
curved form. 

How ii the apparent diamettr of the tun measured 7 What it the magnitude of the 
apparent diameter when the eartk. is farthest from the sun 7 What when nearest 7 What 
is meant by the term perihelion, aphelion, perigee, apogee, apsides, and the line of the 
a jsides 1 Are the places of the perihelion a d aphelion fixed in space 7 



108 THE EARTH VIEWED ASTRONOMICALLY'. 

vation the next year, we should find that the perihelion 
occurred nearly 12" of space (11. 29") to the east of its 
position the year before. 

184. Year after year this motion continues in the 
same direction. The earth therefore, in moving from its 
perihelion to its perihelion next again, a period which is 
termed the anomalistic 1 year, performs one entire revo- 
lution and about 12" over. This small space is con- 
verted into time, as follows: 360° : 365 days 6h. 9m. 
10.7sec, (the length of a sidereal year) : : 11.29" : 4m. 
34.9sec. The length of the anomalistic year is therefore, 
366d. 6k 13m. 45.6sec. 

185. This motion of the perihelion from west to east, 
may be conceived to take place as if the line of the 
apsides had a slow motion from west to east ; or as if the 
earth's orbit, imagined to be a solid elliptical ring moved 
about the sun as a pivot ; the line of the apsides, making 
an entire revolution in about 115,000 years. 

186. This subject is illustrated in Fig. 36, where Aries, 
Taurus, &c, represent a part of the ecliptic, S the sun, 
and AOP, A l O l P l and A 2 2 P 2 , the position of the 
earth's orbit at different times. The aphelion in the 
three positions is at A, A 1 , A 2 , the perihelion at P, P 1 , 
P 2 , and the line of the apsides takes the directions APR, 
A l P l R l , A 2 P 2 R 2 ; the places of the perihelion P as re- 
ferred to the heavens occupying successively the points 
R, R 1 , R 2 , as the line of the apsides moves from west to 
east. Thus though the earth's orbit preserves the same 
form and the earth maintains the same distances from 
the sun at every revolution, yet the orbit itself may and 
does vary its position in space continually. 

187. Apparent Angular Motion. The apparent 
angular motion of the sun in the ecliptic, is obtained from 
observations on its right ascension and declination ; and 
these measurements are made by means of the transit 

1. Anomalistic, from anomaly, an irregularity. 

What is the amount of the annual change in the position of the perihelion? 
In what direction does it movel Is this motion constant "? What is meant by the term 
anomalistic year 1 What is its length ? How may this motion of the perihelion be con- 
ceived to take place ? In how long a time does it take far the line of the apsides to make 
ona revolution 1 Illustrate from figure, How is the apparent angular motion of the sur 
measured 1 



VARIATION IN THE EARTH ORBITUAL VELOCITY. 109 
FIG. 36 




ANOMALISTIC YEAR. 



instrument or mural circle, 1 and the astronomical clock. * 
The daily apparent velocity of the sun at apogee, is 
nearly 57' 12" (57' 11.48",) and at perigee 1° Or, which 
is the same as saying that the earth's actual daily motion 
at her aphelion is 57' 12", and at her perihelion 1° 01'. 

188. Variation in the Earth's orbitual velocity. 
It might be supposed that these variations in the sun's 
apparent daily velocity are entirely owing to the periodi- 
cal changes in its distance from the earth ; since if the 
latter were always to move through its orbit with the 
same speed, its angular velocity would be inversely pro- 

1. The mural circle, is an instrument especially employed for measuring 
arcs on the meridian. It is a graduated circle much larger than that usu- 
ally connected with the transit instrument, and consequently much smaller 
arcs can be measured upon it. It is termed a mural circle, because when 
in its place it is firmly connected with a wall. Murus, in Latin, signifies a 
wall. 

2. It will be recollected that the clock is only used in taking right 
ascensions. 

What is the daily apparent velocity of the apogee "? What at perigee 1 What is this 
the same as saying 1 What might at first be supposed to be the cause of the variations \m 
the earth's orbitual velocity 1 



110 THE EARTH VIEWED ASTRONOMICALLY. 

portioned to its distance from the sun. l But these changes 
in distance will not account for the changes in angular 
velocity to the full extent of the latter ; for the observations 
of astronomers show, that the angular velocities of the 
earth at any two points of its orbit are not to each other 
inversely as the distances, but as the squares 2 of the distances 
at these points, a fact which proves that the earth 
actually moves faster according as it is nearer to the sun. 

189. Form of the Earth's orbit ascertained by 
Angular Velocities. We have just seen that the 
angular velocities at any two points of the earth's orbit are 
inversely as the squares of the distances at these points. 
The square roots 3 of the angular velocities will, therefore, 
be inversely proportioned to the distances.* Observing 
therefore, from day to day, the sun's apparent angular 
velocity, we can thus obtain the relative distances of the 
sun from the earth throughout an entire year ; and hav- 
ing these, we can proceed to map down the figure of 
the earth's orbit in the manner already explained in 
Art. 178. 

190. Product of the Square of the Distance 
into the Angular Telocity. — Constant. From the 
relation that exists between the angular velocities of the 
earth in its orbit and its distances from the sun, it re- 
sults, that if the angular velocity of the earth for any 

1. This fact is easily proved. If from a common centre we describe two 
circles, aud the radius of the larger circle is twice as long as that of the 
smaller, then the circumference of the larger circle will also be twice a? 
long as that of the smaller. Now if two bodies start together the first on 
the smaller circumference and the second on the larger with the same 
velocity ; by the time the first has made one revolution or 360°, the second 
has only made half a revolution or 180°. In other words that body which 
is twice as far from the centre as the other, has only half the angular 
motion of the latter. 

2. The square of a number is the product arising from multiplying the 
number once into itself, thus 4 is the square of 2 ; because 2x2 equals 4. 

3. The square root of a number is such a number as multiplied into itself, 
will produce the first number. Thus the square root of 4 is 2, because 
2x2 gives 4. 

4. If four quantities are in proportion, their square roots will also be in 
proportion ; thus, if 4 : 16 : : 9 : 36, then 2 : 4 : : 3 : 6. 

What do the observations of astronomers show ? What is proved by this fact? What 
can be determined by the angular velocities 1 What results from the relation that exist* 
between the angular velocities and distances. 



PRODUCT OF THE SQUARE, &C. Ill 

given period is multiplied into the square of its distance 
from the sun at that time the product will always be the 
same. 

191. For when one quantity increases at exactly the 
same rate as another decreases, they are said to vary in- 
versely, and their product is always the same. Thus if 
a locomotive passes over a i$iven space with a certain 
speed and in a certain time ; i f the speed is doubled and the 
time halved, or the speed halved and the time doubled the 
same space will still be passes 1 ovfcr ; and this will con- 
stantly be true if one of thes»; two quantities is always 
increased in just the same ratio 1 as the other is diminished. 

192. It follows from this fact, since the angular velocity 
of the earth varies inversely as the square of its distance 
from the sun, that the product of the angular velocity of 
the earth for any given period into the square of its dis- 
tance at that time is invariably the same. Thus, for in- 
stance, the angular velocity for the 20th day of June, 
multiplied by the square of the distance that the earth is 
then from the sun, is equal to the product of the square of 
the distance and angular velocity for the 20th of Decem- 
ber, and so for any other day in the year. 

From the preceding relations another result is also 
obtained, which is expressed in astronomical terms, by 
saying that the radius-vector 2 of the earth descnbes areas 
directly proportional to the times. This expression signi- 
fies, that if the centres of the earth and sun were con- 
nected by a line, and this line moved around the sun as 
on a pivot carrying forward the earth in its orbit ; that 
then the spaces swept over by the line, would exactly cor- 
respond in extent with the times that the line was in mo- 
tion; for instance, that the space passed over by the 
radius- vector in two days is double that swept over in one., 
one-half of that described in four, &c. To illustrate. I*\ 
Fig. 35, where SE is a radius-vector, if the earth is sup 

1. That is, if one of these quantities is multiplied by any number tl 
9ther is divided by the same number. 

2. Derived from the Latin word vector, signifying a carrier. 

What it true in respect to the product of two quantities that are inversely proportional 
What follows from this fact 1 What other result is stated ? What does this exprmio 
signify? Give instances 1 Illustrate from figure. 



112 THE EARTH VIEWED ASTRONOMICALLY. 

posed to describe the arcs SS l and S^ 2 , in the same 
time, bringing the radius-vector successively into the 
positions S'E and S 2 E, then the areas SES 1 and S l ES 3 , 
ire equal. 

KEPLER'S LAWS. 

193. The principle just stated, is one of the laws of 
Kepler. This distinguished astronomer, who flourished 
about 250 years ago, discovered three great laws of 
planetary motion, which from their importance are 
termed the laws of Kepler. They are enunciated as 
follows : 

First Law. The planets move in ellipses around the 
sun, which occupies a focus common to all these ellipses. 

Second Law. The radius-vector describes areas propor- 
tioned to the times. 

Third Law. The squares of the periodic* times of the 
planets are proportional to the cubes' 1 of their average, 
distances from the sun. 

EXTENT OF THE EARTH'S ORBIT. 

194. "We have discovered the form of the earth's orbit 
by ascertaining its relative distances from the sun during 
its annual circuit, but the actual extent of this orbit can 
only be known when we have the real distance of the 
earth from the sun in some known measure as miles. 
In what manner it is computed we will now explain. 

195. How Ascertained. In order to solve prob- 
lems like these mathematicians have taken the circum 
ference of a circle as BDMN, Fig. 37, and divided it into 
arcs of degrees, minutes and seconds, beginning to reckon 
from B. Lines, like XI, X l I l , X 2 I», X 3 I 3 , &c, are then 
drawn, or supposed to be drawn from one extremity of 

1. Periodic time is the time occupied by a planet in performing one 
revolution about the sun. Thus, one year is the periodic time of the earth. 

2. A cube is the quantity resulting from multiplying a quantity into itself 
twice ; thus 8 is the cube of 2 because 2x2x2 equals 8. 

State the laws of Kepler 7 Have we as yet ascertained the dimensions of the earth's 
orbit 1 What have we discovered ? How can the actual extent of the earth's orbit be 
obtained ? 



SUN'S DISTANCE. 
FIG. 37 



113 




CIRCLE WITH TRIANGLES. 



each arc perpendicular to the diameter MB, passing through, 
the other extremity, making with portions of this diameter 
and the several radii, CX, CX 1 , CX 2 , &c, a series 
of right angled triangles; viz., CXI, CX 1 ! 1 , CX 2 P, &c. 
Giving next some particular value to the radius of the 
circle, as a foot for instance, they have calculated in parts 
of the radius the value of the heights, (XI, X 1 ! 1 , &c.,) and 
the bases (CI, CI 1 , &c.,) in as many right angled tri- 
angles as there are seconds in one quarter of the circum- 
ference from B to D. These results set down in order 
with others of the like nature constitute what are termed 
trigonometrical tables. Bearing in mind these facts we 
will proceed to the second part of the explanation. 

196. In Fig. 38, S represents the centre of the sun. E 
that of the earth, SL is a line supposed to be drawn from 
the centre of the sun, touching the earth at L, and 
necessarily at right angles to the radius of the earth LE ; 
and ES is an imaginary line, connecting the centres of the 

Explain the method taken by mathematicians to solve problems like these t 



114 THE EARTH VIEWED ASTRONOMICAL!, Y . 



FIGS. 38 & 




SUNS DISTANCE MEASURED. 



earth and sun. , SLE, therefore, constitutes a right an- 
gled triangle, and the angle LSE is the average hori- 
zontal parallax of the sun, equal to 8". 9. 

1 97 . Now we know the length of LE, which is half the 
earth's average diameter, to be 3,956.2 miles, and as we 
have the value of two angles in the right angled trian- 
gle SLE, we can find that of the third, since the sum of 
the angles of any rectilinear triangle is always equal to 
180 degrees, Art. 13. These things being known we can 
obtain the real distance of the sun by a simple proportion. 
Looking into the trigonometrical tables we select a right 
angled triangle whose angles are respectively equal to 
those in SLE, let CBD, Fig. 39, be that triangle, the 
lengths of whose base, hypothenuse 1 , and heighthaye allbeen 
calculated, and are set down in the tables. But as SEL 
and CBD are similar triangles, the sides about the equal 
angles are proportional (Art. 14,) i. e. the hypothenuse of 
one is to the hypothenuse of the other, as the height of the 
one is to the height of the other ; and so of the bases. To 
obtain therefore, the distance of the sun, we should 
make the following proportion ; namely, BD : CB : : 
LE : SE. 

198. Now we find from the tables that if CB is one 
mile in length, then the value of BD is equal to four 
thousand three hundred and fifteen hundred millionths 



1. Hypothenuse — the hypothenuse of a right angled triangle, is the side 
opposite the right angle. 

Calculate the distance of the sun from the earth 1 



THE SEASONS. 115 

of a mile (.00004315.) Substituting the values of the first 
three terms of the above pro portion, it would stand thus : 
(BD) (CB) (LE) 
(.00004315) : 1 : : 3956.2 : SE 
By the rule of three, SE will therefore equal the pro- 
duct of the second and third terms, divided by the first, 
to wit; 

( 3956.2 x 1 ) 

.00004315 
which gives 91,684,820 miles, for the value of SE, the 
distance of the sun. In round numbers therefore, the 
average distance of the earth from the sun is 92,000,000 
of miles ; at the perigee, it is nearly 90,500,000, and 
at the apogee, 93,500,000. 

The extent of the orbit of the earth is estimated 
at about 600,000,000 miles, 1 and through this immense 
space it sweeps in the course of a year, at the rate of 
nineteen miles per second. 



CHAPTER X 

OF THE SEASONS. 



199. The Seasons. The changes of the seasons, 
depend upon three causes. First, the fact tha,t the sun 
illumines but one half of the earth at a time ; Secondly, 
that the axis on which the earth revolves is inclined to 
the plane of the ecliptic ; Thirdly, that its position at 
any one point in the earth's orbit is invariably parallel 
to its position at every other point. 

1. Though the earth's orbit is an ellipse the eccentricity is very small, 
and we may regard it as almost a perfect circle. Considering the orbit as a 
circle we ascertain its extent by the rule for finding the circumference of 
a circle from knowing its diameter. Multiplying therefore, 190,000,000 
miles by 3.14159, we obtain in round numbers 600,000,000 miles, for the 
.ength of the earth's orbit. 

What in round numbers is the average distance ? What the least and what the great- 
est 1 What is the extent of the earth's orbit 1 What is its orbitual velocity per second 1 
What is subject of Chapter X. ? Upon how many causes does the changes of the se»*ons 
depend ? Nam* them 1 



116 THE EARTH VIEWED ASTRONOMICALLY. 

The axis 1 of rotation is inclined to the plane of 
the ecliptic about sixty-six and a half degrees, and 
constantly points to the same place 2 in the celestial sphere, 
during an entire revolution of the earth in its orbit. For 
although in the interval of six months it shifts its posi- 
tion in space the extent of the diameter of the earth's 
orbit ; viz., one hundred and ninety millions of miles, yet 
this is so small a distance compared with that of the fixed 
stars, that at one of these stars our globe, if it was possi- 
ble to see it, would not appear to move ; the vast area in- 
cluded in its orbit, dwindling down to a mere point. If, 
therefore, the axis of the earth points to any place or star 
in the celestial sphere, it will continue to point to it in 
every position that the earth assumes in her revolution 
about the sun. 

200. By the aid of Fig. 3 40, we shall be enabled to 
perceive how the variety of the seasons is produced by 
the causes just mentioned. In this cut, S l represents the 
sun, the twelve globes indicate the several positions of the 
earth in its orbit, in the successive months of the year 
with the corresponding signs, and the dotted line CS^ 
gives the direction of the plane of the ecliptic. In the 
several globes C is the centre of the earth, DCL is an 
equatorial diameter and shows the direction of the plane 
of the equator ; the diameter at right angles to this ; viz., 
.NCS is the axis of the earth and its extremities the north 
and south poles ; N representing the north pole. The two 
large arcs of circles on each side of DCL, are the tropics 
and the small arcs near the poles the arctic* (northern) and 

1. The axis of the earth is at right angles (90°) with the plane of the 
equator. The plane of the ecliptic being inclined to that of the equator about 
twenty-three and one half degrees, it must therefore be inclined to the axii 
about sixty-six and one half, degrees since sixty-six and one half added to 
twenty-three and one half equals ninety. 

'2. Precession and nutation will of course produce a very slight 
displacement. 

3. The figure is here drawn as if the plane of the ecliptic was viewed 
obliquely, the orbit of the earth therefore, appears more eccentric than it 
actually is. 

4. Arctic (northern.) From the Greek word, arktos meaning beat . 
because the north pole of the heavens is in the constellation called the bear. 

What is the extent of the inclination of the earth's axis to the ecliptic ? Explain why 
the earth's axis is directed to the name points in the heavens notwithstandir^ the eartk 
revolves about the sun ? Exp ain the fieure. 



THE SEASONS. 



117 




118 THE EARTH VIEWED ASTRONOMICALLY. 

antarctic\ (southern) or polar circles. The lines drawn 
in each globe from C, parallel to CS'C, indicate the posi- 
tion of the plane of the ecliptic with respect to that of the 
equator. 

201. Spring. At the vernal equinox, (March,) when 
the earth is in Libra, 2 the circle of illumination extends to 
t the two poles,* the sun is in the plane of the equator, and 

* is seen from the earth in this plane. As the earth rotates 
on its axis every point upon its surface is then half the 
time of one rotation in darkness, and the other half in 
light In this position of the earth, the days and nights 
are therefore equal all over the globe. 

202. Summer. When the earth is in Capricorn at the 
northern summer solstice 4 , (June,) the axis being un- 
changed in direction, the north pole is presented towards 
the sun, and the circle of illumination extends beyond the 
pole N to the arctic (northern) circle, while in the south- 
ern hemisphere it falls short of the south pole S, reaching 
only to the antarctic (southern) circle. 

203. The sun is now seen from the earth in the direc- 
tion CS 1 , having apparently moved towards the north the 
extent of the angle DCS 1 . This angle DCS 1 measures 
the inclination of the plane of the ecliptic to that of the 
equator, which is termed its obliquity, and is equal to 
about twenty-three and one half degrees (more nearly 23° 
27' 37.4".) 

204. The exact distance that the circle of illumination 
now overlaps the northern and falls short of the south pole 

1. Antarctic, from the Greek anti opposite, and arktos, bear, i. e., south. 

2. At the time of the vernal equinox the earth is in Libra, but the sun 
as viewed from the earth appears on the opposite side of the heavens in 
the sign Aries. 

3. In the figure, at the vernal equinox the dark hemisphere of the earth 
is presented to our view, the illuminated hemisphere being toward the sun 
as shown in the globe at Aries. The circumference of the circle of illu- 
mination, both at Libra and Aries is DNLS. 

4. Solstice, from the Latin sol, the sun, and sto I stand, because the 
sun appears at the time of the solstices, neither to move to the north or 
south, but to be stationary as respects these directions. 

At the time of the vernal equinox, what is the position of the circle of illumination in 
respect to the poles 1 In what plane is the sun then situated, and in what plane seen 1 
What is said in regard to the lengths of th« davs and nights at this time 1 What is the 
position of the circle of illumination at the northern summer solstice? What is the ob- 
liquity of the ecliptit ? Its extent ? 



SUMMER. 119 

is equal to the obliquity of the ecliptic ; for since the time 
of the vernal equinox, the sun in his apparent motion 
has departed from the plane of the equator at the same 
rate, that the plane of the circle of illumination has de- 
parted from the poles 1 . The parallels of latitude there- 
fore, to which the circle of illumination extends at the 
summer solstice, and which are termed the arctic and an- 
tartic circles, are each about twenty-three and a half 
degrees from their respective poles. The regions inclosed 
within these circles, are called the frigid zones. 

205. At the time of the northern summer solstice, con- 
tinual day reigns at all those places that are situated 
within the arctic circle, inasmuch as the daily rotation of 
the globe does not carry them without the circle of illumi- 
nation; while over the regions that lie within the antarc- 
tic circle, an unbroken night prevails, because the earth 
in its rotation does not at this time bring them within the 
circle of illumination. It is evident from an inspection 
of the figure, that in the northern hemisphere, since half 
the axis CN falls within the plane of the circle of illumi- 
nation, that the days will increase in length and the nights 
decrease from the equator to the arctic circle, where there 
exists a continual day. In the southern hemisphere, since 
half the axis CS falls without the plane of the circle of 
illumination the days will decrease and the nights increase 
in length from the equator to the antartic circle, where an 
uninterrupted night prevails. 

206. At the vernal equinox, the days and nights as 
we have seen are equal in length. A difference in this 
respect commences as soon as the earth departs from this 
point, which gradually increases up to the time of the 

1. The angles DCN and S'CO, are each equal to ninety degrees being 
right angles. If we take from them the angle S'CN which is common to 
Doth, the two small angles that remain ; namely, NCO and DCS 1 must be 
equal to each other, but DCS 1 is the measure of the obliquity, therefore, 
NCO equals 23° 27' 43.4". The distance of the circle of illumination 
from the south pole is proved in the same way, and the same demonstra- 
tion can be used when the earth is at the northern winter solstice. 

The extent of the arctic and antartic circles, and why? What are the Frigid Zones? 
Where does continual day prevail at the time of the northern summer solstice, and why ? 
Where unbroken night, and why? What is said respecting the lengths of the days and 
nights in the northern hemisphere ? In the southern ? When do these differences is 
'ength begin ? . n 

O 



120 THE EARTH VIEWED ASTRONOMICALLY. 

summer solstice, when the difference in the lengths of the 
days and nights is greatest. 

207. At the summer solstice, the sun's rays fall perpen- 
dicularly upon the surface of the earth ih the direction 
S*C, at a point about twenty-three and a half degrees 
(23° 27' 37.4") north of the equator ; the parallel of lati- 
tude passing through this point is termed the northern 
tropic or tropic 1 of cancer, because the sun as now 
seen from the earth appears in the sign Cancer. 

208. Autumn. As the earth departs from the north- 
ern summer solstice and by degrees comes round to the 
autumnal equinox, (September,) the circle of illumination 
gradually approaches the poles, shortening the days and 
lengthening the nights in the northern hemisphere, and 
producing the contrary effects in the southern. When the 
earth has arrived at the autumnal equinox in the sign 
Aries, the circle of illumination again passes through 
both poles, and the days and nights are once more equal 
in length. 

209. Winter. The earth moving onward in its 
course toward the northern winter solstice, the circle of illu- 
mination also changes its position falling short of the 
north pole more and more, and gradually extending beyond 
the south pole ; increasing the duration of the nights in 
the northern hemisphere and diminishing that of the days / 
while in the southern hemisphere the opposite effects 
are produced. At the winter solstice, when the earth is 
in the sign Cancer, (December,) this change has reached 
its full extent ; the circle of illumination then reaches 
beyond the south pole to the antarctic circle, and the regions 
within this circle now enjoy a continual day. But in 
the northern hemisphere the circle of illumination ex- 

1. Tropic, derived from the Greek trepo, to turn about, because when 
the sun, in its apparent advance to the north, has arrived at a point 
about twenty-three and one half degrees from the equator, it then tui n* 
about and moves toward the south. 

Whea greatest"? How is the position of the northern tropic determined? What is it 
culled 1 What changes take place as the earth moves toward the autumnal equinox f 
What it said of the circle of illumination and of the days and night at the equinox 1 
Describe the changes that occur as the earth moves toward the northern winter solstice 
At the northern winter solstice what is said in reference to the circle of illumination, an^ 
the engths of the days and nights 1 Where does there now reign an unbroken dav 1 



POLAR WINTER;- EFFECTS OF REFRACTION. 121 

tend only to the arctic circle, and the space within tht 
latter is now overshadowed by a constant night 

210. As the earth withdraws from the northern winter 
solstice, and again returns to the vernal equinox, the 
circle of illumination by degrees again approaches the 
poles, and the differences between the lengths of the 
days and nights, grow less and less until they cease to 
exist, when the vernal equinox is attained. 

211. A glance at the figure shows us that the sun at the 
northern winter solstice is seen south of the equator in 
the direction CS 1 . And it is seen at this point as far 
south of the equator as it was north, at the time of the 
northern summer solstice; viz., 23° 27' 37.4". The circle 
of illumination therefore at the two solstices, overlaps 
and falls short of the same pole the same extent of space. 

212. The place where the line S*C falls upon the sur- 
face of the earth south of the equator, is the place of 
that parallel of latitude, which is termed the southern 
tropic and which is about twenty -three and a half de- 
grees (23° 27' 37.4") south of the equator. It is called 

the TROPIC OF CAPRICORN. 

213. That portion of the surface of the earth included 
between the northern and southern tropics is called the 
torrid zone, and those parts that he between the two 
tropics and the arctic and antarctic circles, THE north 
and south temperate zones. 

214. We must bear in mind in this explanation that 
the winter of the northern hemisphere corresponds in time 
with the summer of the southern, and the winter of the 
southern hemisphere with the summer of the northern, 

215. Polar Winters— Effects of Eefraction. 
From what has just been stated, it appears that within 
the polar circle there are long intervals of day and night ; 
while at the poles themselves there is but one day and one 
night, each of six months duration. But several causes 
exist which tend to shorten the dreary winter of the 

Where an unbroken night ? What changes take place as the earth returns to the ver- 
nal equinox ? How far south of the equator is the sun seen at the northern winter sols- 
tice 1 How much does the circle of illumination at the two solstices overlap and fall 
short of the same pole ? How is the position of the southern tropic determined 1 What is 
its extent? What is it called? What is meant by the Torrid Zone? What by the 
Temperate Zones ? What must we bear in mind ? What is evident from the facts that 
btive iust been stated ? 



122 THE EARTH VIEWED ASTRONOMICALLY. 

frigid zones. The. principal of these are refraction arid 
twilight As already stated. Art 36, the refraction in 
these regions is unusually great, causing the sun to ap- 
pear above the horizon when it is really considerably below 
it, and of course shortening the night. 

216. In the case mentioned on page 59 which hap- 
pened in the year 1597, three Hollanders were com- 
pelled to pass the winter at Nova Zembla in K Lat. 
75i°. 

After a night of three months duration, the sun ap 
peared on the horizon, in the south fourteen days sooner 
than they expected it in this latitude, and continued from 
this time to rise higher and higher in the heavens. If 
the sun in this instance appeared fourteen days before it 
was really due, the refraction must have been equal to 
three and a half degrees. 

217. Twilight and its Influence. Twilight 1 is 
chiefly caused by the irregular reflection 2 of the sun's rays 
from the particles of the atmosphere, tuhen the orb is below 
the horizon; and it ceases when the sun is below the hor- 
izon more than eighteen degrees, measured on a vertical 
circle. At the equator where the circles of daily motion 
are perpendicular to the horizon, the twilight is the 
shortest, and continues only an hour and twelve minutes. 
The inclination to the horizon of the sun's apparent daily 
path, affects the duration of the twilight. In all coun- 
tries situated between the equator and the poles, the longest 
twilight occurs at the time of the summer solstice. In lati- 
tude 42° 23' 28" the longest twilight lasts for the space 
of two hours, twenty minutes and thirty-one seconds. 

218. At either pole the sun in its apparent path moves 
parallel to the horizon, and never sinks more than about 
23 \ degrees below it, but until it has passed lower than 
18° the faint glimmerings of twilight do not forsake 

1. The twilight that oecurs in the morning is called the dawn. 

2. Refraction is a partial cause of twilight, but this phenomenon is 
principally due to reflection.. 

What causes exist which shorten the winters of the frigid zones ? What are the 
principal? What is said respecting the extent of refraction in these regions ? State 
what was observed at Nova Zembla, in the year 1597. How is twilight caused 1 When 
does it cease? Where is the twilight the shortest? What •? suid respecting the inch- 
nation to the horizon of the sun's path 1 When is twilight /he longest ? What is th» 
.ength of the longest twilight in Lat. 42° 23' 28' ? 



HEAT — ITtf UNEQUAL DISTRIBUTION, &C. 123 

even these places. The combined effect of refraction and 
twilight in shortening the polar night is so great that at 
the very poles, its duration is only seventy days instead of 
six months ; and even the obscurity that then prevails is 
relieved by the constant presence of the moon, when it 
passes north of the equator ; and likewise by the fre- 
quent and fitful splendors of the northern lights. 

219. Heat — Its unequal distribution over the 
surface OF the Globe — Causes. Since the earth de- 
rives its heat chiefly, if not exclusively from the sun, it 
is evident that the temperature of any region is intimately 
connected with the length or shortness of its days; for 
during the day it is ivarmed and cheered by the solar 
rays, but throughout the night, the soil, and most of the 
objects upon it, rapidly sink in temperature, on account 
of the radiation of their heat into the cooler regions of 
the atmosphere. When therefore the days are short and 
the nights long, the ground loses more heat in the night 
than it receives in the day, and winter prevails. On the 
contrary when the nights are shorter than the days, the 
°arth acquires more heat than it loses, and the seasons of 
flower and fruit smile upon the land. 

220. Another cause of the unequal distribution of 
neat over the globe is the fact, that the rays of the sun 
strike the surface of the earth less obliquely in summer than 
■in winter : thus concentrating more heat on a given sur- 
face in the former season, than in the latter. From this 
cause alone it has been computed that thj heat of sum- 
mer would be nine times greater than that of winter, if 
other influences did not exist which lessen the disparity. 

221. The refraction due to the atmosphere, must also 
be taken into account, for according to M. Bouguer, 
when the sun is vertical above any place, 8,123 rays out 
of every 10,000 actually reach it, while if this luminary 
has an elevation of 50 :> 1 only 2,831 of every 10,000 
arrive at the spot. 

State what is said respecting its effect at the poles ? What is said of the combined in- 
fluences of refraction and twilight in shortening the polar night ? What other mitigat- 
ing influences exist? What is the source of the earth's warmth ? What is the temperature 
of any place intimately connected with? Why? When will winter prevail? When 
iummer ? State the second cause of the unequal distribution of heat ? How much hot- 
ter would summer be than winter from this cause if there wero no counteracting influen 
eet ? What : s the third caus« ? 



124 THE EARTH VIEWED ASTRONOMICALLY. 

222. Thus in Fig. 41, if E represents a point on the 
surface of the earth, EB the plane of the horizon, S the 
position of the sun when its rays fall vertically upon E 

FIG. 41. 




LOSS OF HEAT BY REFRACTION. 

and S l its position when the rays make an angle of 
50° with the horizon at E ; then 8,123 rays out of 10,000 
will reach E when the sun is at S, but only 2,831 when 
it is at S. l 
223. Summer of the Southern Hemisphere not 

HOTTER THAN THAT OF THE NORTHERN. The earth is 

nearer to the sun at its perihelion than its aphelion by 
nearly 3,000,000* of miles, and we should naturally sup- 
pose that on this account the former would receive at the 
perihelion an amount of heat sensibly greater than at the 
aphelion. Moreover since the earth at its perihelion is 
near the northern winter solstice when it is summer in the 
regions south of the equator, it would seem that the sum- 
mer should be hotter in the southern hemisphere than it is 
in the northern. It is however found that the fluctua- 
tions in the earth's temperature, from this cause are very 
slight ; for the investigations of philosophers have proved 

1. It will be remembered that the distance of the sun from the earth at 
the apogee is about 93,500,000 miles, and at the perigee 90,500,000, the 
difference being 3,000,000. 

State what is said respecting its influence, and explain from figure. Why might 
we suppose tl e summer of the southern hemisphere to be hotter thau that of the 
northern ? 



ELLIPTICITY OF THE EARTH'S ORBIT. 125 

that the amount of heat received by the earth is exactly 
proportioned to its angular velocity around the sun. 
Therefore since at the perihelion, the earth moves through 
an arc of 61/ in a day, and at its aphelion through an arc of 
57', the respective daily amounts of heat received by the 
earth at its perihelion and aphelion bear the relation of 
61, to 57; a variation in temperature so small that its in- 
fluence upon the climates of the two hemispheres is 
inappreciable, amid other more potent disturbances. 



126 SOLAR SYSTEM. 



PART SECOND, 

SOLAR SYSTEM. 



CHAPTER I. 

THE SUN. 

224. We now proceed to describe the sun, a vast lu- 
minous and material globe; around which a train of 
planets and comets revolve, constituting with the sun 

the SOLAR SYSTEM. 

225. When the sun is observed through colored 
glasses, which intercept a portion of its heat and lessen 
its dazzling brilliancy, it presents the appearance of a 
perfect circle, whose average angular diameter is 32 3". 
We are not however to suppose that it is flat and round 
like a plate. While we revolve on the earth about the 
sun, the latter at the same time rotates on its axis, and 
yet always appears round; a fact which proves it to be 
a globe like our earth, for it is only a spherical body 
that will appear of a circular form when viewed from 
any direction. 

226. Heal Diameter of the Sun. We have seen 
that the average distance of the sun from the earth is 
about 92,000,000, (more accurately 91,684,820,) and 
that the average apparent diameter is 32' 3'. Know- 
ing these two quantities we are enabled to obtain the 
actual diameter of the orb, by the method explained 
in Art. 198. 

227. In figure 42, we represent the sun by the 
circle S, half the sun's diameter by the line SB, the earth 
by the circle E, and the distance of the centre of the 

What is the subject of Part Second ? What of Chapter I ? What is said of the 
sun ? What form does it present when viewed through colored glasses ? What is its 
average angular diameter ? Is it flat and round like a plate ? What proof have we 
that it is a globe? What two quantities must be known in order to ascertain the 
real diameter of the sun ? 




THE SUN. 127 

earth from the centre of the sun by the line ES, which 
is the hypothenuse of the right angled triangle SEB. 1 

228. We next take them from the trigonometrical 
tables the values of the sides of a triangle similar to SEB. 
LetS'E'B'fig- riGS42and43 . 

ure43,be such 
a triangle, in 
which the an- 
gle S l E l 'B f 
equal to SEB 
is 16' r.5 ; S' 
B'E 1 equal to 
SBE is a right 
angle, and B 1 
S'E 1 equal to 
BSE is 89° 44' . 2 Now if S>E l is one mile, the value of 
S'B 1 , as shown by the tables, Is four thousand six hund- 
red and sixty-one millionths of a mile, (.004661ths of a 
mile.) We thus obtain the following proportion, S*E l 
(lmile) : SE (91,684,820 miles) : : S'B 1 (.004661ths 
of a mile) : the length of SB in miles. Multiplying, 
therefore, the second and third terms together, and divid- 
ing by the first, we obtain the following expression for 
the value of SB, the radius of the sun, viz : 
miles 

91,684,820x.004661 /^ QAO ., 
— ? =427,343 miles. 

1 
Thus the length of the radius is found. The entire di- 
ameter of the sun or twice the radius, is therefore, 
854,686 miles, about one hundred and eight times 
greater than that of the earth. 

229. Size. Since spheres vary in size as the cubes 
of their diameters, it follows that the size of the sun 

1 . SEB is a right angle, because when a line as EB is drawn to the 
extremity of a radius of a circle as B, and also touches the circle at that 
extremity, it makes a right angle with the radius. 

2. Since the sum of the three angles in the triangle SEB is equal to 
180° (Art. 13,) if the value of SBE and SEB are knoum, their sum sub- 
tracted from 180° gives the value of the third angle BSE. 

Find the length in miles of the sun's diameter? 



128 SOLAR SYSTEM. 

is (108) 3 1,259,712 times greater than that of the 
earth. 

230. Mass and Density. It has been found by 
astronomers that the mass of the sun is about 317,000 
times greater than that of the earth. Now, since the 
densities of bodies vary as the masses divided by the 
sizes or volumes, it results that the density of the earth 

• x ±i 4- r*i ix 317,000 , 1 

is to that of the sun as 1 to = ^ ' 719 ; or nearly \. 

The earth, therefore, is about four times as dense as 
the sun. 

231. Force op Gravity at the Sun. The attrac- 
tion of a sphere varies directly as its mass, and in- 
versely as the square of the distance of the attracted 
body from the centre of the sphere. Calling, there- 
fore, the earth's mass 1, and its radius 1, the force of 
gravity at the earth will be to the force of gravity at 

*u 1 • 317,000 ,,.■.-. - , afr l 

the sun as ^ is to -^ n ' - ; that is, as 1 to 27.3. A 

body, therefore, which weighs, at the surface of the 
earth, one pound, would weigh, at the surface of the 
sun, over twenty-seven pounds. 

SOLAR SURFACE. 

232. General Appearance. The surface of the 
sun, as revealed by the telescope, is not uniformly 
bright, but black spots are usually seen, and brilliant 
branching streaks, termed faculce 1 , traverse the disk 2 . 
The rest of the surface has a mottled appearance, and 
consists of luminous masses interspersed with dark 
pores in a continual state of change. 

233. Nature of the Spots. A solar spot usually con- 

1 . From the Latin word facula, a little torch. 

2. Disk, the face of the sun, moon, or a planet, as seen from the 
earth, from the Latin word discus, a quoit. 

What is said respecting the size of the sun compared with that of the earth ? What 
of its mass and density ? Show how we ohtain the force of gravity at the sun as 
compared with that at the earth ? How much would a body, which weighs a pound 
on the earth, weigh at the surface of the sun ? What is the general appearance of 
the solar surface. 



NATURE OP THE SPOTS — EXTENT, &C. 129 

sists of a dark portion, called the umbra 1 or nucleus 2 , sur- 
rounded by a lighter shade, termed the penumbra 3 . Mr. 
Dawes has lately discovered that the umbra in many 
cases consists of two well-defined and separate parts, 
the exterior being less luminous than the interior. 
Sometimes the umbra is seen without a penumbra ; and 
at times the contrary phenomenon occurs. The spots 
are not permanent ; for they often break out suddenly, 
and then as rapidly pass away, their form and size vary- 
ing from day to day, and even from hour to hour. Some- 
times they are seen to divide and break up into sep- 
arate portions, and at others to form in groups of great 
size. The penumbra usually takes the shape of the 
umbra, and their borders, before the spot diminishes, 
are sharply defined. During the contraction of a spot, 
luminous fringes are noticed surrounding the umbra, 
and bright threads of light are seen stretching out 
from these completely across the latter. These lumin- 
ous lines continue to increase and ramify until the 
umbra is covered by the penumbra. The umbra, which 
appears to us as an intensely black spot, is not neces- 
sarily so, its darkness may be simply the effect of con- 
trast with the exceeding brightness of the other portions 
of the sun. In Figs. 44 and 45, spots and clusters are 
shown under their various appearances, the nucleus in 
each being represented by the darkest part, and the 
penumbra by the lightest. Fig. 47 displays the lumin- 
ous fringes, mottled surface, and dark pores of the sun. 

234. Extent, Number, and Periodicity. The spots 
are usually seen in clusters, a single group often contain- 
ing a great number of individual spots. M. Schmidt 
of Bonn, counted no less than 200 in a large cluster 
which he examined on the 26th of August, 1826. 
These groups are often of immense extent ; a cluster 

1. From the Latin umbra, a shadow. 

2. Nucleus, from the Latin word nucleus, a kernel. 

3. Penumbra, from the Latin pene, almost, and umbra, a shadow, i. e., 
a light shade. 

Describe the spots? Are they permanent? Describe the changes incident to them? 
la the umbra necessarily black? Do the spots usually appear singly? 



130 



SOLAR SYaTE:.I. 



observed by Davis, in 1839, was computed to be 186,- 
000 miles long, and to have an area of 25,000,000,000 
square miles. The number of spots varies much in 
different years ; for it occasionally happens that during 



FIG. 44. 



FIG. 45. 





m 



SOLAR SPOTS. 



an entire year spots may be seen on the sun every 
clear day, while, during another year, none may ap- 
pear for weeks, and even months together. 

M. Schwabe of Dessau, infers from the observations 
of 40 years, that the spots have something like a pe- 
riodical increase and decrease in number. The inter- 
val between the times of greatest consecutive frequen- 
cy being from 10 to 12 years. Prof. Wolf of Zurich, 
from a comparison of observations made during the 
last hundred years, concludes that this period ranges 
from 8 to 16 years. 

235. Position. The spots usually occupy two zones 
parallel to the sun's equator, one on either side. Their 
inner limits are a few degrees from the equator, and 
their outer about 35° from it. The late investigations 
of De LaRue, Stewart, and Loewy point to the fact 
that Venus and Jupiter exert an influence on the po- 
sition and magnitude of the spots, for these occur 
nearest to the sun's equator when Venus is in the 
plane of the latter, and are most distant from the so- 

What is said respecting the number in a group, and the extent of the clusters? 
Is the number of spots the same year by year What is said respecting their pe 
riodicity ? What is said respecting the position of the spots ? State the views of 
De LaRue, Stewart, and Loewy in regard to the influence of Venus and Jupiter on 
the position and magnitude of the spots? 



APPARENT MOTION OP THE SPOTS. 131 

lar equator when Yenus attains her greatest solar lat- 
itude. Moreover, when Jupiter and Venus are on the 
same line with the earth, on the opposite side of the 
sun, the spots are larger than when the earth is be- 
tween these planets. A similar influence is exerted 
by Saturn. 

236. Apparent Motion op the Spots. If the sun 
is watched attentively from day to day a spot at its 

FIG. 46. 




SOLAR SPOTS PERIODS OF VISIBILITY AND INVISIBILITY 

first appearance will be perceived on the east side of 
the sun, and is then seen to move gradually across the 
solar disk, until at length it disappears on the western 
side. In this passage it occupies about a fortnight, 
which is the period of its visibility. After about the 
same lapse of time it reappears on the eastern edge. 

This is true with respect to all spots which have 
been observed for this purpose, and whose returns have 
been noted; and the fact that their periods of visibility 
and invisibility are equal, proves that the spots are in 
contact with the sun. For if they were at any consid- 
erable distance from the body of the sun, the time of 
their visibility would be less than that of their invisibil- 
ity, as can be easily shown by the aid of Fig. 46. 

237. In this figure the circle E represents the earth, 
and circle ASB the sun. Now if a spot was not in con- 

What is said of the influence of Saturn ? On what side of the sun does a spot 
first appear? How does it move, and where disappear? What is the period of a 
spot's visibility an\ invisibility ? What is proved by the equality of these periods \ 



132 SOLAR SYSTEM. 

tact with the sun's surface but moved in the large circle 
CDP ; it is obvious that it would be impossible for a per- 
son at E to see it crossing the sun's surface except while 
it was passing through the arc D O. At D and C the spot 
would appear on the edges of the solar disk at B and A, 
and it would be invisible all the time it was passing from 
C through the rest of the circumference of the large circle, 
round to D again. Now as the arc CD is much smaller 
than the other part of the circumference of the large 
circle ; to wit, CPD, the spot, if it moved uniformly 
must be visible for a much shorter time than it is invis- 
ible, which is not the case. 

But if the spot is upon the surface of the sun, it will 
take as long a time for it to move from B to A toward 
E, as from A round to B again; since the diameter 
ASB divides the circumference of circle S into two 
equal parts. The times of visibility and invisibility 
must consequently now be equal ; a conclusion hi gen- 
eral accordance with all observations, 

238. The time that elapses between the appearance of a 
spot at any point on the solar disk, and its reappearance 
at the same point, is therefore about four weeks, (more 
nearly 27 J days.) A spot was observed in the year 
1840, A. D., which made nine revolutions, 

239. Proper Motion. Besides the motion which 
the spots possess in common with the sun, they appear 
to have also a motion of their own. The late rigor- 
ous researches of Carrington, conducted through a pe- 
riod of eight years, from 1853 to 1861, have conclu- 
sively established this fact, and likewise proved that 
those spots near the solar equator move faster than 
those more remote. The motion in solar longitude is 
more marked than that in latitude which is small. 
Near the solar equator the spots sometimes move to- 
ward it, but beyond the parallel of 10° they generally 
move from the equator. The union of these two mo- 

Show from the figure why the spots must he in contact with the sun ? How long 
a time elapses between the appearance and reappearance of the same spot at the same 
point on the sun's surface ? How many revolutions has a spot been known to make ? 
What is said respecting the proper motion of the solar spots ? Which of the two 
proper motions is most marked? 



PACUL^l — PORES, GRANULES, &C. 



133 



tions in longitude and latitude give to the spots a ro- 
tary motion, which has been distinctly observed, and 
which would tend to produce violent commotions in 
the solar atmosphere resembling tornadoes. 

240. Faculae. The bright branching lines, known 
by the name of faculae, and which are the most lumin- 



FIG. 47, 




MJMINOUS FRINGES AND MOTTLED SURFACE OF THE SUN, WITH THE DARK 



ous portions of the sun's surface, are found in the vi- 
cinity of large spots and groups ; and extend over im- 
mense tracts, some of the faculae being 40,000 miles 
long and from 1,000 to 4,000 miles broad. They are 
seen to the best advantage when near the edge of the 
solar disk. 

241. Pores, Granules, Willow Leaves. Within a 
few years the sun has been most diligently observed by 
astronomers, and the latest investigations show that 
the entire luminous surface of the sun is made up of 
bright masses separated by dark intervals or pores. 
These masses are readily revealed by telescopes with 
powers ranging from 130 to 407. 

242. According to Mr. Dawes, these bright portions, 

What is the effect of the union of these two motions, and what would it tend to 
produce? What are faculee ? Where are they found ? What is said of their extent ? 
What do the latest investigations show respecting the sun's surfa.ee ? 



134 



SOLAR SYSTEM. 





FIG 48 






illlllillllflW 


igillilii; 


"mm mm 


WmTv 


,;;; 

: ^ 


iljH 


B 




iHRBlS 


iiPi 




IHHH 


■■H 



GRANULAR OR WILLOW-LEAF STRUCTURE 



which he terms granules, have no definite form, some 
being four or five times the size of others, and differ- 
ing in shape from the form of an arrow head to that 
of a trapezium rounded at the corners. On the other 

hand, Mr. Stone repre- 
sents them as having the 
form of nee grains, while 
Mr. Nasmyth, and Prof. 
Secchi , and other observ- 
ers assert that these 
bright objects have the 
distinct form of ivillow 
leaves, and that the lu- 
minous surface of the sun 
may be regarded as con- 
sisting of these separate 
leaf-like bodies interlac- 
ing each other, the dark pores being the spaces between 
them. Mr. Nasmyth exhibited to the British Associa- 
tion a sheet of black paper, upon which was pasted a 
network of pieces of white paper cut out in the shape 
of willow leaves, which he regarded as truly illustrat- 
ing the structure of the solar surface. The granular 
and willow-leaf form of the masses is shown in Fig. 48. 
243. Rotation of the Sun on its Axis. It is by 
means of the solar spots that the rotation of the sun on its 
axis is ascertained, and the period of its rotation deter- 
mined. The general equality in their times of visibility 
and invisibility, and the uniform direction they pursue 
in their passage across the sun's disk, lead to the con- 
clusion that they are connected with the body of the 
sun, and are all carried forward from west to east by 
the rotation of this great orb on its axis. Astronomers 
have differed somewhat in respect to the period of rota- 
tion, but the best and most careful measurements show 

What are the views of Dawes and Stone in reference to the form of the bright mass- 
es 9 What are those of Nasmyth, Secchi, and others on this point 9 What illustra- 
tion did Mr Nasmyth exhibit to the British Association 9 J low is the rotation of 
the sun on its axis ascertained, and the time of the rotation determined ' What is 
their general motion the same as ? In what time does the sun complete a rotation ? 



ROTATION OF THE SUN ON ITS AXIS. 



that the sun rotates once on its axis in the space of 25 
days 7h. 48m. 

244. This period is less than that of the revolution of 
the spots, and the reason is evident. If a spot is no- 
ticed just on the eastern margin of the sun by a spectator 
upon the earth, it will notreappearwponthe same margin 
when the sun has completed one rotation. For while the 



FIG 49 




PERIOD OF THE SUN'S ROTATION. 

sun has been performing a revolution on its axis the 
earth has also been advancing in its orbit, and the eastern 
margin of the sun is now as many degrees and parts of a 
degree to the west of what was the eastern margin when 
the spot first appeared, as the earth has advanced degrees 
and parts of a degree in its orbit, during a rotation of the 
sun. This angular space over and above a complete 
rotation must be gained before the spot will be seen from 
earth, reappearing on the eastern edge of the sun. 

245. This fact is illustrated by Fig. 49. In this fig- 
ure the circle S represents the sun, and OR a portion 
of the earth's orbit. When the earth is at E, F is a 
point on the eastern margin of the sun ; but when at 

Is this period equal to that of the revolution of the spots ? Explain why they 
differ ? Explain from figure 49 7 



136 SOLAR SYSTEM. 

E 1 , F l is on the eastern margin. Now if the earth was 
stationary at E, and a spot appeared first at F, it would 
remain visible for a time, then disappear ■, and at 
length reappear at F, when the sun had made exactly 
one rotation. 

But the earth is not stationary, for while the sun is 
rotating once it advances as far, we will suppose, as E 1 . 
The spot will not therefore reappear when it has arrived 
at F, and the sun has made one rotation ; the sun must 
revolve still more until the spot has arrived at F l , when 
it will be seen by the spectator at E 1 on the eastern 
margin of the sun ; the same place that it occupied when 
seen at F from E. The time therefore that elapses between 
the appearance and reappearance of a spot is the time it 
takes the sun to perform one rotation, and such additional 
part of a rotation as is represented by the angle FSF. X 
Now the angle FSF 1 is equal to the angular motion of the 
earth in its orbit, while passing from E to E l , viz: the 
angle E l SE ;' a quantity which is known, since the time 
the earth takes in passing from E to E 1 is exactly the 
same as that which elapses between the appearance and 
reappearance of the same spot, viz : about 27-J days. 

246. An approximation to the period of the sun's ro- 
tation may be thus obtained. The earth moves from Eto 
E l in nearly 27 J days, at the rate of about one degree a day ; 
the angle ESE 1 is therefore nearly equal to 27 J°, and so 
is FSF 1 . Consequently the sun in 27 J days performs 
one rotation (360°) and the additional part FSF 1 (27 J°.) 
We then have the following proportion. The angular 
space through which the sun rotates in twenty-seven and a 
quarter days, to wit: 387 J° is to 27 J days as 360° is to 
the period of one rotation. . Multiplying next the second 
and third terms and dividing by the first, thus 
360x27J 
387J 



1. The triangles EFS and E^S being in every respect equal, the an- 
gles E^F 1 and ESF, are therefore equal. Taking from these the an- 
gle ESF 1 which belongs to both, the remaining angles ESE 1 and FSF 1 
must also be eijual to each other. 

Knowing the period of time that elapses between the appearance and return of a 
spot, how do we obtain the time of the sun's rotation? 



INCLINATION OP THE SUN'S EQUATOR, &C. 137 



the value of the fourth term is found to be 25£ days. 
The period of rotation is therefore, about 25 days 8h. 
More refined calculations give the period before men- 
tioned, viz: 25 days Vi. and 48m., as the true time of 
the sun's rotation on its axis. 

247. Inclination of the Sun's Equator to the 
plane op the Ecliptic. If the equator of the sun was 
coincident with the plane of the ecliptic, it is clear that 
the path of the spots across the disk of the sun would ap- 
pear as straight lines, when viewed from the earth in 
any point of its orbit. 

If the plane of the sun's equator was perpendicular 
to that of the ecliptic, it is manifest that in tivo opposite 
positions of the earth and 
in two only would the 
paths of the spots appear 
as straight lines, viz : — 
when the plane of the sun's 
equator passed through the 
earth ; and when the poles 
of the sun's axis were di- 
rected to the earth, the 
spots would be visible 
throughout their entire 
revolution, and would de- 
scribe complete circles. — 
But the spots present no 
such phenomena in their passage across the sun, con- 
sequently the plane of the surfs equator is neither perpen- 
dicular to nor coincident with that of the ecliptic. 

248. The paths of the spots however vary when 
viewed from different points of the earth' s orbit. At the 
close of November and the beginning of December they 
appear as straight lines. They then gradually assume 
more and more of an oval shape, being most curved 
about the first of March. From this time their curvature 
diminishes , until the last of May or the first of June , when 
the appear again as straight lines. They pass through 

State what would be the form of the paths of the spots if the equator of the sun 
was coincident with the plane of the ecliptic ? What if perpendicular. Describe the 
paths actually pursued by the spots ? 




INCLINATION OF THE SUN'S EQUATOR TO THE 
ECLIPTIC. 



138 SOLAR SYSTEM. 

the same changes for the next six months, with this differ- 
ence, that the curves are noiv in a direction opposite to 
that which they took for the six preceding months. 

249. By observing the changes in the paths of the 
spots with great attention, astronomers have been en- 
abled to ascertain the position of the solar equator with 
i efcrence to the plane of the ecliptic, and the result is that 
the former is inclined to the latter at an angle of about 
seven and a quarter degrees ; as shown in Fig. 50, where 
PEP'Q represents the sun, PP 1 its poles and EQ its 
equator, which makes with FC, the direction of the 
plane of the ecliptic, an angle of about 7J degrees. 

NATURE OF THE SUN. 

250. The views now adopted regarding the constitu- 
tion of the sun are based upon the analysis of the spec- 
trum. What this analysis is will now be explained. 

251. Spectrum Analysis. When a beam of solar 
light passes through a prism the light is refracted, and 
forms an oblong image called the solar spectrum, which 
consists of seven colors, viz: violet, indigo, blue, green, 
yellow, orange, and red. When the spectrum is viewed 
through a telescope it is seen to be crossed by numer- 
ous dark lines, very unevenly distributed. The distin- 
guished philosopher, Fraunhofer, discovered 590 dark 
lines between the red and the violet, and thousands 
have been discerned by other observers. Fraunhofer 
designated the most important of these lines by the 
letters of the alphabet, and also ascertained that for 
solar light their position and grouping were invariable, 
whether the direct light of the sun was analyzed, or 
the reflected, as that from the moon or Venus. The 
spectra of the fixed stars are also crossed by dark 
bands, but they differ in their systems of lines, not 
only from the sun, but from each other. 

252. Spectra of Flames containing Metallic and 
other Yapors — Bright Lines. It has been found that 

How is the inclination of the sun's equator to the plane of the ecliptic determined? 
How much does this inclination amount to ' What is said of the Tiews now held in 
regard to the constitution of the sun ? What is the solar spectrum ? State what is 
said respecting the dark lines? What is observed in regard to the dark lines in all 
solar light, whether direct or reflected ? What is said of the spectra of the fixed stars? 
What is noticed in the spectra cf flames containing metallic vapors ? 



DARK LINES HOW CAUSED. 139 

flames in which different substances are vaporized pre- 
sent spectra crossed by bright lines, and that their re- 
spective systems of lines are so peculiar in regard to 
number, color, and position, that each substance can be 
recognized by its lines. Thus if zinc is vaporized, its 
spectrum is crossed by bright bands of red and blue, 
while strontium gives six red lines, with one of orange 
and another of blue, and calcium one broad green band, 
and an orange band with several smaller orange lines. 

253. Experiments of Bunsen and Kirchoff. A few 
years ago an investigation of the bright lines of arti- 
ficial spectra was most elaborately and carefully con- 
ducted by Kirchoff and Bunsen, and in order to map 
down the positions of the bright lines of the metals, 
they employed the dark lines of the solar spectra as 
guides. Upon comparing the various spectra with that 
of the sun, they were surprised to find that the entire 
systems of bright lines coincided exactly with certain 
groups of dark solar lines. Thus the bright lines of 
sodium, magnesium, lithium chromium, nickel, and 
iron, corresponded exactly with the same number of 
dark lines in the solar spectrum. The spectrum of 
iron brings out this correspondence very distinctly; for 
this metal furnishes 60 conspicuous bright lines, which 
coincide precisely in position, grouping, and breadth 
with the same number of dark solar lines. 

DARK LINES. 

254. Dark Lines — How Caused. The spectrum of 
a flame containing metallic vapor is crossed, as has 
been already stated, by bright lines, but if upon this 
flame is poured a more brilliant light, giving a contin- 
uous spectrum, the bright lines are changed into dark 
lines. Thus a gas flame, charged with the vapor of so- 
dium, gives two bright yellow lines, which are changed 
into dark ones, when the intense electric light, which 
gives a continuous spectrum, is made to shine upon 
the gas flame. This phenomenon is explained upon 

What is said respecting these systems of bright lines ? State m detail the discov- 
eries made by Bunsen and Kirchoff? Explain how the bright lines of the spectrum 
may be changed into dark lines, and give the explanation of this change? 



140 SOLAR SYSTEM. 

the principle that a body which has the power of emitting 
any particular color, has also the power of stopping that 
color. Thus the portions of the sodium flame which give 
the bright yellow lines have the power of stopping the 
yellow color of the same refrangibility in the electric 
light. The spectrum formed by the two lights is far more 
brilliant than that formed by the gas flame alone, and 
the yellow color of the electric light being stoppd, the 
yellow lines of the sodium become relatively dark. 

255. Metals found in the Sun. From a thorough 
comparison by Kirch off, Bunsen, and others, of the so- 
lar spectrum with various metallic spectra, it appears 
that the bright lines of about fifteen metals exactly 
correspond in number, arrangement, and position with 
the dark lines and bands of the solar spectrum. These 
metals are 



Sodium, 


Iron, 


Zinc, 


Manganese, 


Calcium, 


Chromium, 


Strontium, 


Aluminium, 


Barium, 


Nickel, 


Cadmium, 


Titanium. 


Magnesium, 


Copper, 


Cobalt, 





Peculiar masses of solar light also exhibit the bright 
lines of hydrogen. Vaporized iron, as stated, gives sixty 
marked bright lines, which coincide exactly in position, 
grouping, and breadth with the same number of dark 
lines inthespectrumof the sun. Kirchoff has calculated 
that the chances against an accidental agreement in this 
case are as 1 to 1,000,000,000,000,000,000. The con- 
clusion is therefore reached that these metals, and pos- 
sibly others, exist in the sun in a state of vapor, and 
that the arrangement of the metallic flame illumined 
by the electric light is presented in this orb on a most 
magnificent scale. 

256. Physical Constitution of the Sun. From all 
the observations which have been made upon the sun, 
both in its ordinary condition and when eclipsed, it is 
inferred that the sun consists of a central intensely hot 
nucleus, above which is an atmosphere filled, apparent- 
state the results obtained by Kirchoff, Bunsen, and others, from a comparison of 
the solar spectrum -with various metallic spectra? What metals exist in the sun? 
What is said respecting the bright lines of iron ? Is this coincidence accidental ? 
What is therefore inferred ? Of what does the sun consist ? 



PHOTOSPHERE LXTERIOR ATMOSPHERE. I'll 

ly, with white hot solid particles, distributed in the form 
of vast clouds over the whole surface of the central 
body. And that outside of this powerfully luminous 
atmosphere, is another less bright and heated gaseous 
stratum, charged with the vapors of a variety of bodies, 
chiefly metallic in their nature. 

257. Photosphere. The white hot clouds, which 
are the luminous masses that have been variously de- 
scribed as resembling, in shape, rice grains, willow leaves, 
and so forth, constitute the visible body of the sun, and 
are called the photosphere. These clouds arc supposed 
to be produced by the condensation of the metallic and 
other solar vapors, somewhat as the clouds in our at- 
mosphere are caused by the condensation of the aqueous 
vapors. Although such a condensation implies a loss 
of heat, it is not at variance with the view that the 
photosphere may be very hot, since we are speaking of 
temperatures the lowest of which possesses an intens- 
ity of which we have scarcely any conception. It may 
seem at first sight to involve an inconsistency to sup- 
pose that the outer atmosphere should be charged with 
metallic vapors, while the condensed vapor forms the 
clouds of the hotter photosphere ; but our atmosphere 
presents analogous phenomena, since in the higher re- 
gions invisible aqueous vapor exists, while clouds are 
formed in the lower and warmer strata. 

258. Exterior Atmosphere or Chromosphere. The 
gaseous atmosphere of the sun extends far beyond the 
photosphere, for during total eclipses rosy masses of 
light are seen rising thousands of miles above the pho- 
tosphere. During the eclipse of 1869, Mr. Hilgard 
observed a mass of this kind 100,000 miles high and 
20,000 wide, analogous in structure to the most delicate 
clouds. It is not impossible that the atmosphere should 
extend hundreds of thousands of miles beyond the solar 
surface. As the light from these red columns is not 

What is the photosphere ? How is it supposed to be formed ? If thus formed, can 
the photosphere be hot? What is said respecting an apparent inconsistency in this 
theory? What is stated in regard to the exterior solar atmosphere? How is this 
proved by observations during total eclipses of the sun ? What is said of the extent 
of the solar atmosphere? How do the observations upon these rosy masses of light 
corroborate the received theory of the nature of the sun ? 



142 SOLAR SYSTEM. 

subjected to the action of the light of the photosphere, 
since they are seen outside of it, they ought, according 
to the above theory of the constitution of the sun, to 
give spectra crossed by bright lines. The observations 
of Lockyer and Jansen on the eclipse of 1868, and those 
of Dr. Peters, Prof. Young, and others on that of 1869, 
show that this is the case. The bright lines observed 
are those of hydrogen in combustion. 

259. Cause of the Spots. The observations of 
astronomers from the time of Dr. Wilson (1769,) to 
the present date, ccnclusively prove that the spots 
are cavities in the photosphere. According to Kir- 
choff, Stewart, Huggins, and others, a spot is caused 
by a downward current from the comparatively cold 
outer atmosphere meeting in the photosphere, with a 
hot ascending current. By this union, portions of the 
photosphere, sinking in temperature, are supposed to 
lose some of their brightness, and to become dark 
in comparison with other parts. It is claimed that 
this view explains the appearance of facula? near a 
spot, and all the gradations of darkness in the penum- 
bra and nucleus. If we bear in mind, however, that 
between the luminous clouds that form the photosphere, 
dark spaces or pores are always seen, we have only to 
suppose that by some of those tremendous commo- 
tions, which are common to the sun, the clouds are 
driven apart and the pores widened, and then all the 
phenomena of a spot would occur. The central part 
of the pore, whether a portion of the surface of the 
interior solar mass or not, rendered dark by contrast 
would become the nucleus, while its borders, overlaid 
and fringed by delicate films of luminous matter, would 
present the lighter shades of the penumbra. 

260. Nature op the Facul^e. The faculas are re- 
garded as portions of the photosphere elevated above 
the general surface, and in the photographs of the solar 
spots which have been taken by De La Rue, they ap- 

What are the spots ? How are they caused according to the views of Kircboff, 
Stewart, Huggins, and others ? Would a separation of the clouds of the photosphere 
by a violent ccnimotion give rise to the phenomena of spcts ? 



THE MOON — HER DISTANCE. 143 

pear as luminous ridges surrounding the spots. They 
are supposed to be uplifted by currents ascending from 
the central mass. 

261. Solar Disturbances — Their Influence on the 
Magnetism of the Earth. One of the most striking in- 
stances of this influence occurred on the 1st of Sep- 
tember, 1859. For while Messrs. Hodgson and Car- 
rington were then observing a large group of spots, two 
intensely bright faculse suddenly appeared in front of 
the cluster, and within five minutes, spread over a space 
of nearly 34,000 miles. Simultaneously with their ap- 
pearance, the magnetic needle was violently agitated 
throughout the globe, and hours passed before the 
earth resumed its ordinary magnetic state. 



CHAPTER II. 

THE MOON. 

262. This beautiful orb is a constant attendant of the 
earth in its circuit about the sun, revolving meanwhile 
in the same direction from west to east around the earth as 
its centre. Her influence upon our globe, is by no means 
unimportant. Equal in apparent size to the sun, her 
mild splendor dissipates the shades of night, while her 
attractive power sensibly affects the motions of the earth, 
and sways the tides of the ocean. 

268. Distance. This orb is the nearest to its of all 
celestial bodies, her average distance being about 239,000 
miles. The measurement of this distance is obtained in 
the same way as the distance of the earth from the sun. 
The parallax of the moon is found to be about 57', and 
the length of the earth's radius being known, the calcu- 
lation is made as follows. 

264. Let M Fig. 51, represent the centre of the moon, 
E the surface of the earth, O its centre, OE a radius ; and 
MO and ME, lines drawn from the moon's centre to the 



What are faculae , and how do they originate ? Is the magnetism of the earth affected 
by solar disturbances ? Relate the instance given. What is the subject of Chapter 
Second ? What is said respecting the motions of the moon, and her influence upon our 
globe ? What is said in regard to her distance from the earth ? How far is she from the 
earth ? How is her distance in niiies ascertained .' W hj,t is the amount of her parallax ? 



144 SOLAE SYSTEM. 

earth's centre and surface , we thus have a triangle in 
which MEO is a right angle, EMO 57', and MOE 89" 

FIG 51. 




MOON S DISTANCE MEASURED. 

3'. 1 We now select a similar triangle ; suppose MVEW 
to be such a triangle, and that the side WO 1 is one 
mile long, then the trignometrical tables show us that 
O l E l must be sixteen thousand Jive hundred and eighty 
millionths of a mile long {.016580,) and we establish from 
the sides of the similar triangles the following propor- 
tion ; to wit, .016580 (O'E 1 ): 1 (WO 1 ) : : 3956.2 2 
(OE) : 238,613 miles (MO.) The fourth term, found by the 
common rule of three, is the distance of the moon from the 
earth's centre measured in miles. When all the niceties of 
calculation are introduced into the computation the 
average distance is found to be 238,650 miles. 

265. Diameter in Miles. In the same manner the 
diameter of the moon in miles is ascertained, when we 
have first learned her distance in miles. For if we repre- 
sent the moon's centre, Fig. 52, by L, and the earth's by 
E, and imagine two lines drawn from the centre of the 
earth ; the one to the moon's surface at S, and the other 
to her centre, these lines will form with the moon's 
radius LS a right angled triangle ; whereof ESL is the 
right angle, SEL the apparent semi-diameter of the moon, 
equal to 15'' 33 //3 and LE the moon's distance from the 

1. The sum of the angles MEO and EMO subtracted from 18(P gives 
a remainder of 89° 3' ; i'e. the value of MOE. 

2. The mean length of the radius of the earth is 3956.2 miles. 

3. The mean apparent diameter of the moon is 31 '6". 

Explain from the cut how the distance is circulated? What is the exact distancol 
Bhow how the diameter of the moon in miles is ascertained ? 



DIAMETER IN MILES. 
FIG. 52. 



J45 




MOON 8 DIAMETER IN MILES. 



earth ; all known quantities. Selecting then a similar tri- 
angle; viz., L^E 1 , and regarding L*E l as one mile long, 
we find that according to the table the length of L^S 1 is 
four thousand jive hundred and twenty-three millionths 
of a mile (004523.) We then make this proportion ; 
to wit, (L'E 1 ) 1 : (S'L 1 ) .004523 : : (LE) 238,613 : 
1079. Half the diameter of the moon therefore measures 
1079 miles, and the entire diameter is 2158 miles, which 
is nearly its true length. 

When the calculation is carried out with the greatest 
exactness, and every refined correction made, the moon's 
diameter according to Prof. Madler is found to be 2,160 
miles long ; an extent a little greater than one fourth of 
the eartKs diameter The relative sizes of the earth and 



FIG. 53. 




RELATIVE BIZEB OF THE MOON AND EARTH. 

moon are shown in Fig. 53, where E represents the eariS 
and M the moon. 

What is the extent of the riitimeter 1 



146 SOLAR SYSTEM. 



MOON'S PHASES. 



266. The moon has no light of her own, but shines by 
the reflected light of the sun, the hemisphere presented to 
the sun being illumined with his rays while that which 
is turned from him is shrouded in darkness. The relative 
positions of the sun moon., and earth are not always the 
same, and hence arise those changes in the appearance 
of the moon which are termed phases. 1 

FROM NEW MOON TO THE FIRST QUARTER, 

267. At new moon the centres of the sun, moon, and 
earth, are situated in nearly the same straight line, the 
moon being now between, at which time she is said to 
be in conjunction. In this position the unenlightened part 
of* the moon is turned towards the earth, and the orb is 
Jost to our view. In a short time it advances so far to 
the east of the sun as to become visible in the west soon 
after his setting. Its bright portion then appears of a 
crescent form, on that side of the disk which is nearest to 
the sun, while the remaining dark part of the disk is just 
discerned, being faintly illumined by the earth-light. 2 
In this position the convex part of the moon's crescent is 
towards the sun, and the line which separates the illumined 
from the unillumined part, called the terminator, is 
concave. 

268. Each succeeding night the moon is found farther 
eastward of the sun, and the bright crescent occupies 
more and more of her disk, the terminator gradually 
growing less curved, until when the moon is 90° distant 
from the sun, half the disk is illuminated and the termi- 
nator becomes a straight line ; the moon is then in her 

1. Phases from the Greek word phasis, meaning an appearance. 

2. Earth-light. Some of the light which falls upon the earth from the 
sun is reflected to the moon, and a portion of this is reflected back again 
from the moon's surface to the earth. This is the earth-light. The 
amount thus reflected from the lunar surface must necessarily be very small, 
but it is sufficient to enable us faintly to discern the outlines of the moon. 



Does the moon shine by her own light? What is the cause of the changes in t.'«e 
appearance of the moon? What tin tie is given these changes? Describe the phases 
of the moon from new moon to Mie fir-t quarter. 



FKOM THIRD QUARTER TO NEW MOON. 147 

FIRST quarter. The extremities of the moon's crescent 
are balled cusps, l and from the time of new moon to the 
first quarter the moon is said to be horned. 

FROM THE FIRST QUARTER TO FULL MOON. 

269. As the moon advances beyond her first quarter, 
the terminator becomes concave toward the sun and more 
than half the lunar disk is illuminated, when the moon is 
said to be gibbous. 2 At length in her easterly progress, 
she reaches her second quarter, and the sun, earth, and 
moon are again in nearly the same straight line; the 
earth however being now between. The moon is now in 
opposition, 180° from the sun, rising in the east at about 
sunset; and as her whole enlightened dish is turned 
toward the earth, she is now at the FULL. 

FROM FULL MOON TO THE THIRD QUARTER. 

270. After opposition the enlighted part of the moon 
again becomes gibbous as she returns toward the sun ; and 
she rises later and later every night. When she has 
arrived within 90° of the sun, she is then in her 
third quarter, the terminator is once more a straight 
line, and the bright portion of the orb again fills up one 
half of the disk. 

FROM THIRD QUARTER TO NEW MOON. 

271. After passing her third quarter the moon resumes 
her crescent shape, rising early in the morning before the 
sun. As her time of rising approaches nearer and 
nearer to that of the sun, the glittering crescent contracts 
in breadth, until at length the moon arriving again at 
conjunction its light entirely disappears. The positions 
of the moon where she is midway between any two ad- 
jacent quarters are termed her octants* 

1. Cusps, from the Latin word cuspis, meaning the point of a spear. 

2. Gibbous from the Latin word gibbus, meaning swelled out. 

3. Octant, derived from the Latin word octo, eight ; an octant being 
distant from its adjacent quarters, one eight part of the moon's orbit, or 45°. 

From the First Quarter to the Full 1 From the Full to the Third Quarter 1 From the 
Third Quarter to New Moon 1 What are the octants 1 



148 



SOLAR SYSTEM. 



This subject is further illustrated by Fig. 54, where 
S8, SI, and all lines parallel to these indicate the direc- 
tion in which the sunbeams come, and E represents the 



FIG. 54. 




MOON'S PHASES. 



earth. The circles 1, 2, 3, 4, 5, 6, 7 and 8, show the places 
of the moon in her orbit ; at conjunction (1,) the first 
octant (2,) the first quarter (3,) the second octant (4,) at 
opposition (5,) the third octant (6,) the third quarter (7,) 
and at the fourth octant (8 ;) while the white portions of the 
circles l 1 , 2 1 , 3 1 , 4 l ,'5 l , 6 1 , 7 l and 8 l , exhibit the phases 
of the moon in all the preceding positions. Thus when 
the moon is at the first octant (2,) the phase corresponding 
to this place is displayed in circle 2 1 , that of the first 
quarter (3,) in circle 3 l ; and so of all the other positions. 
272. The points in the moon's orbit where she is in 
conjunction and opposition are called the syzygies 1 , and 
those where she is 90° from the sun the quadra- 
tures. 2 Fig. 55, exhibits the appearance presented by 

1. Syzygies, derived from the Greek words, sun, with and zeugos, a 
yoke, i.e. a yoking or joining together. 

2. Quadratures, derived from the Latin word quadrans, meaning a 
quarter. 

Explain Figure 54. What are the syzygies and the quadratures 1 What does Figure 55 
exhibit. 



MOON'S QUADRATURE. 
FIG. 55. 



149 




moon's quadrature. 



150 SOLAR SYSTEM. 

the moon in quadrature when seen magnified through a 
telescope. 

273. What the Phases Prove. The phases of the 
moon clearly prove that this body possesses a spherical 
figure, and is illumined by the sun ; for it is only a sphe- 
rical body, which viewed in the positions we have men- 
tioned can exhibit the phases that the moon has displayed 
through all past time. This point may be illustrated in 
the following manner. If in the evening we place a 
lamp upon a table, and, taking our stand at a distance, 
cause a person to carry around us a small globe, we 
shall perceive that the illumined part of the globe, in its 
circuit around us, presents to view all the phases of the 
moon. Being crescent shaped when the globe is nearly 
between us and the lamp ; in its first quarter when the lines 
drawn to it from the eye and the lamp make a right 
angle ; and at the full, when it is opposite to the lamp : 
and so on throughout the entire circuit. 

274. Sidereal Month. Upon observing the moon 
from night to night, we perceive that she has a motion 
among the fixed stars ; for if on any particular evening 
she is beheld near a star, on the next succeeding clear 
evening, she will be seen^/ar to the east of this star. And 
thus the moon continues to advance from west to east 
until, in the space of 27 days 7h. 43m. ll|sec, she makes 
one entire revolution, occupying the same position among 
the stars as she did at the commencement of this inter- 
val. For this reason the period of time j ust mentioned is 
denominated a sidereal month. 

275. Synodical or Lunar Month. The time that 
elapses between two consecutive full moons or new moons, is 
termed a synodical 1 month, and consists of 29 days 12h. 
44m. 3sec. If the earth was stationary while the moon 
revolved around it, the length of the synodical month 
would exactly equal that of the sidereal, for the moon in 
passing from conjunction, would then be brought round 

1 . Synodical. Derived from two Greek words sun, with or together 
with, and odos a journey. In union signifying a coming together. 

What do the phases prove ? Is the moon stationary or in motion ? How is she proved 
lo be in motion? In what direction does she move? How long is she in completing a 
revolution from west to east? What is this period termed, and why ? What is meant by 
u synodical or lunar month ? What is its length ? 



SYNODIC AL MONTH. 151 

to conjunction again at the completion of one revolution. But 
as it is, while the moon is revolving around the earth, the 
earth is at the same time revolving about the sun in the 
same direction ; and the moon in passing from one con- 
junction to the next, must necessarily describe more 
than one complete revolution. And the same remark is 
likewise true in respect to any two consecutive phases, as 
for instance from the third quarter to the next third quar- 
ter. In fact in passing from conjunction to conjunc- 
tion, the moon describes not simply 360° or one entire 
circumference, but about 389° 6', or nearly one circumfer- 
ence and a twelfth ; and the time which she occupies in 
going through 389° 6', is a synodical month, or 29 days 
12 hours 44 minutes and 3 seconds. 

276. This subject may be illustrated, as were the 
lengths of the solar and sidereal days (Art. Ill,) by the 
movements of a watch. Let us call the centre of the dial 
plate the sun, the end of the minute hand the moon, the 
end of the hour hand the earth, and the 12 o'clock mark a 
fixed star. At twelve o'clock the ends of the hands and 
the centre of the dial are in a straight line, or all together ; 
the end of the hour hand (the earth,) is now between the 
end of the minute hand (the moon) and the centre of the 
dial (the sun,) and the imaginary moon is in opposition. 
An hour afterward the end of the minute hand (the moon,) 
is again at the 12 o'clock mark which represents the 
fixed star, and has made one complete circuit, which we 
can call a sidereal month. But it is not in opposition for 
the end of the hour hand which represents the earth is 
in advance, and the opposition will not take place until 
the minute hand overtakes the hour hand, when the centre 
of the dial and the ends of the pointers will be again in 
the same straight line; and this event occurs at 5m. 
27 T 3 T sec. past one o'clock. One hour in this illustration, 
therefore, represents a sidereal month, and one hour five 
minutes and twenty-seven three elevenths seconds a synodical 
month. 

Why longer than a sidereal month ? How many degrees does the moon pass through 

in the period of a synodical month? Illustrate this subject by the movements of 

a watch ? What length of time in this illustration represents a sidereal, what a 

H/nodical month ? _ . 

7* 



152 SOLAR SYSTEM. 



PHYSICAL ASPECTS OP THE MOON. 



277. "When the moon is full we perceive, even with the 
naked eye, that her dish is not uniformly bright, but that 
marked alternations of light and shade extend over the en- 
tire surface. By the aid of the telescope these peculiari- 
ties are more distinctly developed, and ranges of moun- 
tains are seen and dusky tracts, which the early astrono- 
mers regarded as seas. These tracts, however, are 
most probably broad plains and precipitous valleys, for 
there is strong evidence that but little moisture exists 
in the moon, and close observation moreover shows, 
that these regions are too rugged to be sheets of water. 

278. Dr. Dick remarks, " I have inspected these spots 
hundreds of times, and in every instance gentle elevations 
and depressions were seen, similar to the wavings and 
inequalities which are perceived upon a plain or country 
generally level." The surface of a sea or ocean would 
present no such appearances. 

279. The proof that the surface of the moon is very 
uneven, rising into lofty mountains, and sinking into deep 
valleys, is quite conclusive. In the first place the termi- 
nator, which it will be recollected is the line that sepa- 
rates the illumined part of the disk from the unillumined, 
and is in fact the profile of the moonh surface, is not a regu- 
lar unbroken line. Such it would be if the surface of the 
moon was smooth, but it is rough and jagged, as seen in 
Fig. 55 ; thus revealing the existence of prominences and 
depressions in the lunar surface. 

280. Moreover, near the terminator long shadows fall 
opposite to the sun within the illumined regions ; a fact 
which can only be accounted for by the uprising of moun- 
tains which intercept the rays of this luminary ; just as 
on the earth lofty peaks and pinnacles cast extended 
shadows at the rising and setting of the sun. 

281. When the moon is increasing, it is sun rise at 

When the moon is full, what appearances does her disk present to the naked eye? 
What when seen through a telescope ? What views were entertained by the early astron- 
omers 1 Are these tracts, seas or mountains ? What does Dr. Dick observe 1 Would 
the surface of a sea present the aspects noticed by Dr. Dick t What facts are stated in 
Arts, 279 and 280, that prove the surface of the moon to be rough, rising into mountain* 
and sinking into vulleys 1 



LUNAR MOUNTAINS. 158 

those parts of the illumined region which lie near the 
terminator ; and as the terminator advances beyond the 
mountains here situated, and the sun rises higher and 
higher, the shadows of these mountains gradually shorten. 
In the same manner as the mountains of the earth pro- 
ject long shadows at sunrise which rapidly contract as 
the sun ascends the heavens. 

282. At full moon no shadows are seen, for the light 
from the sun falls vertically upon the lunar mountains. 
If the moon is waning the shadow of any mountain is 
observed to lengthen by degrees as it approaches the ter- 
minator; being the longest when this boundary is reached. 
When the mountain arrives at the terminator it is there 
sunset. The shadows of our own mountains undergo 
the same changes as the day declines. 

283. Lastly, beyond the terminator, within the unenlight- 
ened parts, bright spots or islands of light are seen (Fig. 55,) 
which must be the tops of mountains. For since the light 
of these spots is that of the sun reflected from the moon's 
surface, these luminous points catch the solar rays only 
on account of their being more elevated than the contiguous 
regions, that are veiled in obscurity ; and the farther these 
spots are from the terminator, the higher must the moun- 
tains be. 

284. If the moon is increasing, it is sunrise on these 
summits while the dawn prevails below ; but if decreas- 
ing it is sunset, while twilight reigns at their base. In 
the same manner, the peaks of the Alps glow with the 
first rays of the sun, and around them play the last lin- 
gering beams of his rosy light. 

285. Lunar Mountains. The mountainous regions 
of the moon present a greater diversity of arrangement 
than those of the earth. Eugged and precipitous ranges 
are seen, as on our globe, traversing the lunar surface in 
all directions ; but the moon possesses besides a peculiar 
mountain formation, termed ring mountains, which are 
detected in every part of her visible surface. 

What is said respecting the shadows when the moon is increasing ? What of them 
when the moon is full ? What when waning ? What fact is adduced in Art. 283, 
which shews that the surface is rugged ? When is it sunrise on these summits, and when 
tunset ? What is said respecting the mountainous regions of the moon ? 



154 SOLAR SYSTEM. 

A wide plain, and often a deep cavern or crater, 1 is 
beheld encircled by a chain of mountains like a ring. 
These latter in many instances rise to a great altitude ; 
and frequently from the middle of the enclosed plain a 
lofty insulated peak shoots far up into the sky. 

286. Impossible as it may appear, the heights of many 
of the lunar mountains have been calculated, and we 
shall now proceed to show one of the ways in which 
the calculations are made. 

287. Height Measured. In Fig. 56, let S represent 

FIG. 56. 




the position of the sun, E that of the earth, and M the moon 
in her first quarter, the hemisphere OD which is turned to 
the sun being enlightened, and the other CP being dark. 
CL is a lunar mountain, the top of which is illumined by 
the light of the sun, coming in the direction of the ray 
SOL ; and this mountain top consequently appears to 
a spectator at E, as a bright spot, surrounded by the 
darkness of the unenlightened hemisphere. 

288. When the moon is in quadrature, as in the figure, 

1. Crater. Derived from the Greek word krater, which signifies a bowl. 

Have the heights of the lunar monntains been measured? Explain one of the method* 
•unloved for estimating the heights ? 



HEIGHT MEASURED. 155 

trie line EOM, drawn from E to the centre of the moon, 
makes a right angle with the sun-ray SOL, which touches 
the terminator at 0, and strikes the top of the mountain 
at L. 

289. Now an observer at E, sees the top of the moun- 
tain in the direction of the line EL, and with the proper 
instrument he can easily ascertain the magnitude of the 
angle LEO ; which is the angular distance between the 
summit of the mountain and the terminator. Having 
obtained this value, and knowing the apparent diameter 
of the moon, and its length in miles ; the height of the 
mountain (CL) can be ascertained by means of a property 
of the right angled triangle LOM; viz., that in every 
right angled triangle the square of the hypothenuse 1 is equal 
to the sum of the squares of the other two sides. 

290. The calculation is made as follows. Let us sup- 
pose that the angle LEO is equal to one twelfth part of 
the apparent radius of the moon (15' 40" ;) then will 
the line LO be very nearly equal to one twelfth part of 
the moon's radius measured in miles ; viz., 90 miles. 
Now the square of LM equals the square of LO 
(90 x 90,) added to the square of OM (1080 x 1080 ;) that 
is to 1,174,500. The square root of this quantity, or 
1083.74 is therefore, the length of the line LM in miles. 
LM is then 1083.74 miles long ; but it consists of two 
parts, to wit, the height of the mountain LC, and the ra- 
dius of the moon CM. Now the length of the latter is 
1080 miles, subtracting then 1080 miles (CM) from 
1083.74 miles (ML,) the remainder 3.74 miles (LC,) is 
the height of the mountain ; nearly three miles and three 
quarters. 

291. It is not necessary that the moon should be m 
quadrature in order to determine, by this method, the 
height of the lunar mountains, but this phase has been 
selected because the calculations are shorter and less m- 
tricate, than when the moon is in other positions in her 
orbit. 

A distinguished German astronomer, Schroeter, has 

] . The hypothenuse of a triangle is the side opposite the right angle. 
Show how the calculation is made 1 



156 SOLAE SYSTEM. 

pursued a different method from the one just given. He 
estimated the altitudes of the moon's mountains, by the 
length of the shadows cast upon its surface. 

292. Names and Heights of the Lunar Moun- 
tains. The method now universally adopted, by the 
most distinguished astronomers, to designate remarkable 
regions in the moon, is to assign to these localities the 
names of men renowned for their attainments in science 
and literature ; as for instance, Newton, Tycho, Kepler, 
Herschel. 

293. The surface of the moon is more rugged than that 
of the earth ; for though the former is much smaller 
than the latter, yet its mountains nearly equal in altitude 
the highest of our own. 

294. Prof. Madler of Prussia, who has studied the 
physical condition of the moon with more success than 
any living astronomer, has constructed, in connection 
with Prof. Beer, another Prussian astronomer of high 
reputation, large lunar maps; in which the most re- 
markable spots and regions of the moon are laid down 
with great exactness. Their magnitudes have also been 
ascertained, and their forms delineated with the utmost 
precision. 

295. The heights of no less than 1095 lunar mountains 
have been determined by these astronomers, and out of 
twenty measured by Madler, three tower to an altitude of 
more than 20,000 feet, while the rest exceed the height 
of 16,000 feet, or about three miles. The names of a few 
of the loftiest mountains are as follows : 

Feet. Feet. 

Newton, 23,800 Casatus, 20,800 
. Curtius, 22,200 Posidonius, 19,800. 

296. The highest lunar mountain, as we perceive, 
reaches an altitude of nearly 24,000 feet, or about four 
miles and a half; which is nearly the height of the lofti- 
est mountains of our globe. If our mountains were as 

How did Schroeter estimate the heights of the lunar mountains 1 What method has 
been adopted in order to designate the remarkable regions in the moon 1 What is said 
-especting the surface of the moon? State what has been done by Profs. Madler and 
Beer 1 How many lunar heights have been determined by these astronomers ? What is 
said respecting the heights of twenty, measured by Madler ? Give the names and altitude* 
of the four highest? 



LUNAR CRATERS. 157 

much higher than the lunar as the earth's diameter is 
greater than the moon's, the Himmalehs and Andes 
would rise to altitude of 16| miles, above the level of 
the ocean. 

297. Lunar Craters. The moon is not only dis- 
tinguished for lofty mountains, but also, as we have 
stated, for singularly formed cavities and craters which 
are depressed far below the general surface. They are 
of various sizes, and are scattered all over the disk of the 
moon ; being however most numerous in the southwest- 
ern part. In form they are nearly all circular, and are 
shaped like a bowl ; and from the level bottom of most 
of the larger a conical hill usually rises at the centre. 

298. Oftentimes the circular walls of these craters are 
entirely below the general surface of the moon, but they 
are usually elevated somewhat above the surface, forming 
a ring mountain; whose height on the outside is frequently 
not more than one-third or one-half of its altitude on 
the inside ; measuring from the bottom of the crater to 
the top of the mountain. 

Twelve craters according to Schroeter are more than 
two miles deep, and to some of these a depth of o vox four 
miles is assigned by the same observer. 

299. That these appearances, which are regarded as 
cavities are such in reality, is evident from the fact, that 
the side nearest the sun is in shadow, while the side most re- 
mote is illumined by his beams. Just as the eastern side 
of a well is in shadow in the morning, when the sun 
shines, while the western side at the top is bright with 
the solar rays. 

300. One of the finest instances of a ring mountain 
with its enclosed crater is the spot called Tycho. The 
breadth of the crater is nearly fifty miles, the height of 
the mountain on the inside is about 17,000 feet, and on 
the outside it is not less than 12,000 ; the bottom of the 
crater, is therefore 5,000 feet below the general surface 
of the moon. 

If the mountains of our globe were as much higher than the lunar mountains as the 
earth is larger than the moon, how high would the Andes and Himmalehs soar 1 What it 
said respecting the lunar craters ? Of their sizes and forms ? What is said in regard to 
the circular walls of these craters 7 How deep are these craters according to Schroete 
State the proofs that these spots are really cavities. Describe Tycho ? 



158 



SOLAR SYSTEM. 



Another remarkable ring mountain is Copernicus, the 
diameter of whose crater is more than 55 miles. 

301. By the aid of a powerful telescope, Copernicus 
is seen as delineated in Fig. 57. The ranges of the 




A RING MOUNTAIN WITH ITS CRATER, (COPERNICUS.) 



ring "mountain are here beheld on the right hand of 
the figure, with their summits bathed in light, while 
their sides opposite to the sun, rest in the deepest shade. 
On the left hand, nearest to the sun, the solar rays, 
streaming over the encircling mountain walls of the 
crater, leave half of it in darkness ; the heavy shadow 
of the central mountain projecting far into the illumined 
portion. 

302. Many of the craters are of great dimensions, the 
largest being nearly 150 miles in diameter. The diame- 

Explain the cut. What is said respecting the magnitude of these craters ? 



LUNAR VOLCANOES. 159 

ters of the six broadest as inferred from the observations 
of Prof. Madler, are as follows : 

Miles. Miles. Miles. 

149 143 127 

115 113 96 

And of 148 craters whose diameters were measured by 
the same astronomer : 



2 


were 


between 


1 


and 


2 i 


niles 


wid 


7 


u 




u 


2 


« 


3 


a 


u 


16 


11 




a 


3 


a 


4 


a 


(( 


19 


« 




u 


4 


u 


5 


a 


a 


17 


u 




it 


5 


u 


6 


tc 


a 


18 


(( 




« 


6 


u 


7 


a 


u 


11 


it 




u 


7 


u 


8 


a 


a 


G. 


a 




it 


8 


a 


Q 


(( 


u 



12 " " 9 " 10 " " 

And 36 were above 10 miles across. 

303. Lunar Volcanoes. The existence of active 
volcanoes has been announced more than once by as- 
tronomers. In 1787, Sir William Herschel, gave notice 
to the world that he had observed three lunar volcanoes in 
actual operation, two of which were either just ready to 
break out, or were nearly extinct ; while the third was 
in a state of eruption. The burning part of the latter was 
estimated to be three miles in extent, while the adjacent 
regions were illumined with the glare of its fires. Since 
this period the attention of many astronomers has been 
directed to this subject, and their investigations have led 
to the conclusion that the remarkable appearances, which 
were regarded as indicating the existence of volcanoes, 
can be satisfactorily attributed to other causes, and the 
opinion is now prevalent among astronomers, that active 
lunar volcanoes do not now exist. 

304. The aspects of the moon however, indicate that 
it has been the theatre of intense volcanic action, and the 
ring mountains or craters strikingly reveal this fact. " In 
some of the principal craters," says Sir John Herschel, 

Give the diameters of the six broadest, according to Madler's measurements? State 
what is said of the diameters of 148 craters measured by the same astronomer? What 
was the belief of Sir William Herschel in respect to the existence of active lunar volcn 
noes? Have these remarkable appearances been regarded as active volcanoes by luter 
astronomers? What is now the prevalent opinion among astronomers ? Are there any 
indications in the aspects of the moon that active volcanoes once existed ? 



160 SOLAR SYSTEM. 

*' decisive marks of volcanic stratification, arising from 
successive deposits of ejected matter, may be clearly 
traced with powerful telescopes." There is a striking 
resemblance between the surface of the moon and of the 
volcanic regions of the earth which abound with extinct 
craters, as shown by the cut upon the opposite page. 

305. Lunar Atmosphere. On this subject the opin- 
ions of astronomers have been much divided. Many 
have maintained its existence, while others have denied 
it altogether. Schroeter, the eminent German astron- 
omer, before mentioned, who observed the moon with 
great care, and under the most favorable circumstances, 
detected & faint light like that of twilight, extending a 
short distance from the horns of the moon over her 
dark portions, which are turned away from the sun. 
This he attributed to the presence of an atmosphere rising 
about a mile in height from the surface of the moon. 
When the moon passes between us and a star the rays 
of the latter would be refracted as they passed by the 
edge of the moon if she possessed an atmosphere like 
that of the earth, and the star would be visible when 
actually behind the edge of the moon. It would dis- 
appear later and re-appear earlier than it would if the 
moon had no atmosphere. Numerous and skilful ob- 
servations which have been made on this phenomena 
have failed to detect so slight an amount of refraction 
as 4". In the opinion of Prof. Madler, however, this 
orb possesses a thin atmospheric envelope of variable 
extent, and astronomers are now generally disposed 
to admit, that a lunar atmosphere exists ; but so rare, 
that if it is constituted like that of the earth it is 
nearly two thousand times lighter. The pressure of our 
atmosphere is counterpoised by a column of mercury 
30 inches high ; but the pressure of the lunar atmos- 
phere would be sustained by a column of mercury 
about ^th part of an inch in altitude, and would be less 

State the remarks of Sir John Herschel. What are the views of astronomers re- 
specting the existence of a lunar atmosphere ? What did Schroeter detect ? If the 
moon possessed an atmosphere of much density what effect would refraction pro- 
duce ? What is the opinion of Prof. Madler, and other astronomers on this subject ? 
What must be the density of the lunar atmosphere compared with the density of our 
own ? How high a column of mercury would support it '{ 




EXTINCT VOLCANOES OF AUVERGNE, FRANCE. 




LUNAR SURFACE AS SEEN THROUGH A TELESCOPE. 



To face paze 160. 



moon's orbit. 161 

dense that the air remaining in a receiver, after exhaus- 
tion by an air pump of the best construction. 

Whenever the moon is seen in an unclouded sky her 
brightness is always the same, neither speck nor vapor 
dimming the mild effulgence of her orb. From this 
circumstance it is inferred that the moon is destitute of 
water ; otherwise, evaporation would ensue, and clouds 
would form and float in the lunar atmosphere. Indeed, 
the extreme rarity of the moon's atmosphere precludes 
the supposition of the existence of water. The waters 
of our globe are kept from wasting away through evap- 
oration by the pressure of our heavy atmosphere ; but 
the lunar atmosphere exerts so slight a pressure, that 
the waters upon the surface of the moon, if they ever 
existed, would have speedily been converted into vapor. 
And if, as some astronomers imagine, the vapors had 
been removed by some extraneous causes, the moon 
would ever after possess the characteristics which she 
now has ; namely, a dry and steril soil and a bright and 
cloudless atmosphere. 

306. Lunar Heat. In 1856, Prof. Piazzi Smyth found 
that on the Peak of Teneriffe, more than 10,000 feet 
above the sea, the heat of the full moon was only equal 
to that of a common candle 15 feet distant. At the 
general surface of the earth no heat can be detected. 

307. Bulk — Mass — Density. The bulk of the moon 
is equal to ^th part of the bulk of the earth, and her 
mass or quantity of matter is equal to ^ th part of that 
contained in our globe. The moon's density is a little 
more than one-half of the density of the earth. 

MOON'S ORBIT. 

308. By measuring the diameter of the moon from 
day to day, astronomers have discovered that the appa- 
rent size of the lunar disk is subject to variations ; the 

What illustration is given to show its extreme rarity ? What is said regarding the 
brightness of the moon ? What is inferred from this ? Why ? Why is the rarity of 
the lunar atmosphere incompatible with the existence of water ? If it once existed 
what would have beeome of it ? If the vapors had been removed, what result would 
have followed ? What is said respecting lunar heat ? What is the bulk of the moon 
compared with that of the earth ? Her mass ? Her density ? What is said respecting 
the apparent size of the moon ? When the moon crosses a star what is the result of 
the observations that have been made ? 



162 SOLAR SYSTEM. 

greatest apparent diameter of the moon being 33' 32", 
and the least 28 / 48". These changes are evidently 
due to the circumstance that the moon is nearer to the 
earth at one time than another ; the apparent diameter 
being inversely as the distance, (Art. 177.) 

309. Its Figure determined. Taking then the 
daily angular velocities of the moon in her orbit, and her 
daily variations in apparent size, we can determine the 
figure of her orbit in the same way as we ascertained 
that of the earth, (Art. 178.) By mapping down the 
differing lengths of the radius vectors and their angular 
distances from each other, we find the orbit of the moon 
to be an ellipse, with the earth in one of the foci. The 
orbit of the moon deviates more from a circle than that 
of the earth. 

310. The changes in the moon's apparent size prove, 
that when she is nearest to the earth, or at her perigee, 
her distance may be as small as 225,560 miles ; while 
at her most remote point from the earth, or her apogee, 
her distance may increase to 251,700 miles. So that 
the variation in the moon's distance from us amounts to 
26,000 miles ; an extent of space exceeding the circum 
ference of the earth. 

311. The same results are obtained from the changes 
that take place in the horizontal parallax of the moon, 
these changes being also inversely as the distances, (Art. 
95.) The greatest horizontal parallax, according to Biot, 
is 61 / 29" and the hast 53' 51", while the mean parallax 
is 57' 4". 

312. Plane of the Moon's Orbit — Its Inclination. 
The plane of the moon's orbit, is inclined to that of the 
earth's (the ecliptic) at an angle of about 5° 8'. This in- 
clination is not always the same, being sometimes greater 
and sometimes smaller than this quantity. The varia- 
tion is however trifling, never exceeding 23". 

What is the greatest apparent diameter 1 What is the least ? Explain the cause of 
nese variations ? How is the figure of the moon's orbit determined ? What is its figure ? 
How does it compare with the orbit of the earth in respect to its ethpticity 7 What is the 
distance of the moon from the earth at her perigee, as proved by the changes in her apparent 
size 1 What at her apogee ? How much does the variation in distance amount to ? In 
what other way are these results obtained 1 What is the greatest horizontal parallax of 
the moon, according to Biot 1 What the least ? What the mean ? What is the inclina- 
tion of the plane of the moon's orbit to that of the ecliptic ? Is this inclination alwavt 
the same 1 What is the extent of the variation ? 



LINE OF THE NODES. 



163 



313. The Line of the Nodes. The moon in mak- 
ing one revolution about the earth comes twice into the 
plane of the earth's orbit. These two positions, when the 
centre of the moon is at the same time in the plane of 
the ecliptic, and in that of her own orbit, are called the 
moon's nodes. 1 A line joining these two points, is in 
both these planes, and is termed the line of the nodes. In 
Fig. 58, EO represents a part of the plane of the earth's 
orbit, MM the moon's orbit, A and B the moon's nodes, 
and AB the line of the nodes. 

FIG. 58 




LINE OF THE NODES. 



314. The centre of the moon, at each revolution about 
the earth, meets the ecliptic in a different place from that 
in which it met it at the preceding revolution. Thus if 
on the 15th day of June, the node was at A, Fig. 58, at 
the end of the next revolution the centre of the moon 
would be in the plane of the ecliptic, to the west of its 
former place, and the node would be at A 1 . In the suc- 
ceeding revolution it would be at A 2 , and so on. In 
like manner the other node would shift along from B to 
B 1 , B 2 , &c, and the line of the nodes would take the succes- 
sive positions AB, A ! B l , A 2 B 2 , and so on. The line of 
the nodes thus appears to revolve from east to west, and 
this phenomenon is called the retrogression or going back 
of the nodes ; because they shift in a direction contrary 
to that in which the heavenly bodies generally move. 

1. From the Latin word rodus, meaning a knot, a connection. 

What is meant by the moon's nodes? What by the line of the nodes? Explain the 
figure. Are the nodes fixed in space ? Explain from figure. In what direction does the 
line of the nodes appeur to revolve * What is this phenomenon termed? 



L64 SOLAR SYSTEM. 

315. The line of the nodes retrogrades about 3' 10" 
daily, and in the course of 18 years 218d. 21h. 22m. 
46sec., it makes the entire circuit of the ecliptic ; so that, 
at the termination of this period of time, it occupies 
exactly the same position in space as it did at the 
beginning. 

316. Line of the Apsides. If, when the moon is at 
her^en^ee and apogee, we were to measure the angular 
distances of these points from either of the moon's nodes, 
and continue to do so for several successive revolutions, 
we should find that these distances constantly varied. 
The places of the perigee and apogee shifting along the 
lunar orbit from west to east, and the imaginary line 
joining these two points, called the line of the apsides, 
necessarily revolving in the same direction. 

317. This motion is so rapid that the line of the apsi- 
des completes an entire revolution in 8 years 310d. 13h. 
48m. 53sec, so that the perigee occupies the place in the 
lunar orbit that the apogee did about 4 years 155 days 
before; and returns to the place in the lunar orbit 
whence it started, at the end of the longer period just 
mentioned. 

318. The motion of the line of the nodes, and that of the 
line of the apsides may be illustrated as follows : Let us 
first take a round bowl, Fig. 59, and fill it with water to 
the brim, and in the next place an elliptical ring ABC, 
which we place in the bowl, inclined to the surface of 
the water at an angle of about 5°. This ring may rep 
resent the moon's orbit, A her perigee, the surface of the 
water the plane of the ecliptic, and E, F the intersecting 
points of the orbit of the moon with the ecliptic, namely 
the nodes ; EDF is the line of the nodes, and ADB the 
line of the apsides. Now if we make the ring to revolve 
on its centre D in the direction from A towards E, always 
preserving the same inclination to the surface of the 
water ; while at the same time it is made to slide round 
on the edge of the howl in the contrary direction EGF, at 

What is the daily amount of retrogradation ? In what period does the line of the node 
make a complete revolution? Are the moon's perigee and apogee stationary as respect! 
her nodes ? In what direction do they move ? What is the line of the apsides, and how 
does it move 1 In what period would this line make a complete circuit 1 Explain by the 
ad of Figurr 59, the motion of the line of the nodes and of the apsides. 



INCREASED APPARENT SIZE OF THE MOON, &C. 166 
FIG. 59. 




MOTIONS OF THE NODES AND APSIDES. 

about half the rate at which it revolves on its centre, we 
can roughly represent both the motion of the line of the 
nodes, and that of the line of the apsides. For it is evi- 
dent, first, that the supposed line of the nodes EDF, 
would revolve in the imaginary plane of the ecliptic, 
crossing it in all directions ; and secondly, that the line 
of the apsides ADB would also revolve in any opposite 
direction in the plane of the lunar orbit, cutting the line 
of the nodes at all angles, being at one time perpendicu 
far to it, and at another coincident with it. All which 
motions and changes in position, are in accordance with 
the lunar phenomena just described. 

319. Increased apparent size of the Moon when 
in the Zenith. When the moon is in the zenith she is 
nearer to us than when upon the horizon. 

This fact is evident from the inspection of Fig. 60, 
where HOZD, is a portion of the moon's daily path, M 
her position in the zenith to a spectator on the earth at 
P, and M 1 her position on the horizon; the line HH l 
being in the plane of the horizon. 

Now calling E the centre of the earth, EM, the dis- 
tance of the moon when in the zenith, is equal to EM 1 , 
her distance from the centre of the earth when on the 
horizon ; and EM 1 is very nearly equal 1 to PM 1 , which 
is the distance of the moon on the horizon from a spec- 
tator on the surface of the earth at P. PM 1 is there- 

1. The difference in the distances PM 1 and EM 1 is only about thirty 
miles. 

Does it make any difference in the distance of the moon from us whether she is in the 
senith or upon the horizon ? In which position is she nearest to us 1 Prove it from Fig. 60 



166 SOLAR SYSTEM. 

fore nearly equal to EM, but PM, the distance of the 
moon in the zenith from the spectator at P, is shorter 

FIG. 60 




MOON 8 APPARENT SIZE INCREASED IN THE ZENITH. 

than EM by PE, the radius of the earth, and is there- 
fore less than PM 1 by about the same quantity. 

320. The moon is therefore nearer the spectator when 
she is in the zenith than when she is upon the horizon by 
almost 4,000 miles. This change in distance of course 
affects her apparent size, and it is found by measure- 
ment that the breadth of the moon is ¥ V th part greater 
at the zenith than at the horizon, a result which verifies 
the preceding demonstration. For since the moon's dis- 
tance is inversely as her apparent diameter she ought 
when in the zenith, to be gVth of her distance nearer the 
earth than when upon the horizon. Now since her 
average distance from the earth is about 240,000 miles, 
F Vth of her distance is 4,000 miles, which is the length 
of the radius of the earth in round numbers, and is 
nearly equal to the difference of the distances PM and 
PM 1 . 

321. The Moon always turns the same face 
towards the ~Ea rth. Every observer whose attention 
has been drawn to the fact, has noticed that the appear- 
ance of one full moon is almost exactly like that of an- 
other. There is the same relative arrangement of light 

By how much is she then nearer to us? Does this change in distance affect her appa- 
rent size? How much greater is her apparent size when she is at the zenith than 
when she is upon the horizon 1 What does this verify 1 Show in what way J 



LIBRATION IN LONGITUDE. 167 

and shade, and the most remarkable features, such as 
prominent mountains and valleys, are constantly seen in 
nearly the same positions on the moon's disk. This is 
indeed true in respect to all the lunar phases ; for the 
surface of the moon as seen at her first quarter, is that 
which has been seen at every first quarter since the 
creation, and the same which will be seen at the same 
phase, as long as the sun, moon, and earth endure. 

322. This singular phenomenon can be explained only 
on the supposition, that the moon rotates on her axis in 
about the same time that she completes a sidereal revolution 
around the earth ; for if she did not thus rotate we should 
see the greater part of her surface in the course of a 
month ; which is not the case. 

323. This point may be thus illustrated. We will 
suppose a person standing in the middle of a floor, and 
another walking around him in a circle, holding up at a 
level with his eye, a globe, of which the surface of one 
hemisphere is painted black, and that of the other white. 
The first person represents a spectator upon the earth, 
the circle in which the second walks the orbit of the 
moon, the globe is the moon, and the white surface the side 
that she constantly presents towards the earth. Now it 
is manifest, that it the second person walking round the 
circle wishes the spectator at the centre to see nothing 
but the white surface of the globe, as he performs his circuit, 
he must turn the globe round on its vertical axis, at 
exactly the same angular rate that he himself is moving in 
the circle. Thus when he has moved through one quar- 
ter of the circle, the globe must have turned one quarter 
of a circle, when he has traversed one half of the circle, 
the globe must have turned half round ; and so on 
through the entire circle. 

324. Libration in Longitude. If the person hold- 
ing the globe does not always walk at the same pace, but 
sometimes moves at a slower, and sometimes at a faster 
rata than the uniform speed at which the globe rotates on 
its axis, the spectator at the centre will see a little of the 

How does the appeamnce of the moon at any phase during any one month, compure 
with her appearance at the .tame phase, during any oilier month ? How can this phenom- 
enon be explained 1 Give the illustration 1 

8 



168 SOLAR SYSTEM. 

dark hemisphere, first on this side, and then on that ; and 
thus a little more than a hemisphere will fall into view in 
the course of a revolution. 

325. Now a similar phenomenon occurs in respect to 
the moon, inasmuch as she moves uniformly on her axis, 
but not so in her orbit; and therefore we can see at 
times beyond the average boundaries of the moon's disk, 
to the extent of a few degrees of surface on the east and 
west sides. 

At one period a spot, which was visible a little before 
on the eastern side, disappears, while others are seen on 
the western side, which were not previously discerned. 
Ere long the latter pass beyond the illuminated hemis- 
phere, and vanish ; while the former reappear on the 
bright surface. 

326. This apparent motion is called the libration 1 of 
the moon in longitude, because she undergoes a 
change in position as if, while balancing upon her axis, 
she swung backwards and forwards from east to west and 
from west to east ; in which direction, longitude is reck- 
oned on the earth. 

327. Libration in Latitude. The axis about which 
the moon rotates, though always maintaining the same 
direction in space, is not quite perpendicular to the plane 
of her orbit, but is inclined to it at an angle of about 
88i° (88° 27' 51".) Consequently, in certain positions 
in her orbit, we see a little space beyond one of the lunar 
poles and a little distance short of the other ; each pole 
appearing and disappearing in its turn. Just as a spec- 
tator upon the sun, at the time of the northern summer 
solstice, could look about 23|° beyond the north pole of 
the earth, while all the region within the same distance 
of the south pole would then be lost to his view : the 
reverse occurring at the northern winter solstice, all the 
southern frigid zone then coming into sight and the north- 
em disappearing (see Fig. 40.) A small space therefore 

1. Libration^ from the Latin word libratio, meaning a poising or 
balancing. 

Explain libration in longitude ? Why is this motion so termed ? What is the inclina 
tion of the moon's axis to the plane of her orbit ? What phenomenon is -aused bv thi» 
inclination 1 Give the illustration 1 



LENGTH OF THE LUNAR DAY. 169 

around each of the poles of the moon is concealed from 
view or presented to our sight, according as this lumi- 
nary is in one or another part of her orbit. 

328. This phenomenon is termed libration in latitude, l 
because the change in the visible surface takes place in 
a direction from the moon's equator, and terrestrial lati- 
tude is reckoned in this manner. 

329. Diurnal Libration. It is towards the centre of 
the eartli that the moon presents the same face, and she 
would at all times do so to a spectator situated in the 
line joining the centres of the earth and moon, if the li- 
brations of longitude and latitude did not exist. But it 
is only when the moon is on the meridian that we are 
nearly in the line of the centres. When she is upon the 
eastern horizon we, standing upon the earth's surface, are 
elevated nearly 4,000 miles above this line, and overlook 
portions of the lunar surface, which are invisible when 
the moon is on the meridian. 

330. And the same is true when she is upon the west- 
ern horizon, only the change then occurs on the opposite 
side of the lunar orb ; since the upper side of the moon 
at her rising, is the lower at her setting. These varia- 
tions in the aspect of the moon happen daily, and the 
phenomenon is termed the diurnal libration. At the 
moon's rising and setting the diurnal libration is greatest, 
since the spectator can not attain any higher elevation 
above the imaginary line uniting the centres of the earth 
and moon, than when the latter is upon the horizon. 

331. Length of the Lunar Day. The moon, as 
we have seen, rotates on her axis in the same period that 
she completes a sidereal revolution about the earth, mov- 
ing forward in the meanwhile with the latter around 
the sun, through an arc of nearly 27°. Owing to these 
two motions the average length of the day at the moon, 
reckoning by solar time, is equal to the length of a synod- 
ical month, that is to about 29 i of our days (29 days 

1. These variations in the moon's visible surface seem to arise as if her 
axis vibrated to and from the earth. 

What is this phenomenon called, and why? Explain what is meant by diurnal libra, 
tion ? When is it greatest? What is the meuo length of the lunar day measured by on 
days? 



170 SOLAR SYSTEM. 

12h. 44m. 2.9sec.) The mean lengths of daylight and 
night are therefore respectively equal to nearly 15 of our 
entire days of 24 hours duration. 

332. At the lunar equator the days and nights are of 
equal length, each being about 354 hours and 22 minutes 
long, (14d. 18h. 22m. 1.5sec.,) but they vary with the lati- 
tude. Thus at the lunar latitude of 45° the extent of the 
longest day 1 is 354h. 19m., and that of the shor test 35 lh. 
20m. ; while at latitude 88°, the longest day has a dura- 
tion of 449h. 28m., and the shortest of 259h. 16m. 

333. The appearance of the Earth as seen from 
the Moon. To the inhabitants of the moon (if any 
there are,) our earth is seen as a moon of immense size, its 
apparent surface being sixteen times greater than that of 
the sun as he appears to us. For this reason a vast 
amount of light must be reflected from our globe to the 
moon, and all the varied lunar phases which we behold 
would be exhibited by the earth to a lunar spectator 
with a wonderful radiance and distinctness, but in an 
inverse order. Thus when it is new moon to us it would 
be full earth to an observer on the moon, and when full 
moon here, new earth tiiere. 

334. Another remarkable difference also exists. The 
moon is seen by us occupying various positions in the 
heavens, as she displays her successive phases ; but the 
earth would appear to an inhabitant of the moon to be 
fixed in the heavens, during all her periodical fluctuations 
of light. The cause of this singular phenomenon is 
easily explained. The moon turns on her axis from 
west to east just as the earth does, but an inhabitant of 
the moon would be as unconscious of its rotation, as we 
are of the rotation of the earth. Accordingly, as with 
us, the sun and the other fixed heavenly bodies would 
appear to him to be moving from east to west, at the 
same rate that his own orb rotates on its axis. Such 
would be the apparent motion of the earth to a specta- 

1. The word day is here used in distinction from night. 



What the respective lengths of day and night at the lunar equator? What the dura 
lion of the longest and shortest days at the lunar latitude of 45° 7 What at 8S° ? How 
would our earth appear to an inhabitant of the moon? In what order woulr the phase* 
of the earth be exhibited 1 



ACCELERATION OF THE MOON'S MOTION, &C. 171 



tor upon the moon, if the earth teas actually stationary ; 
but this is not the case, for our globe advances from west 
to east in her orbit, just as rapidly as the rotation of the 
moon tends to give it an apparent retrograde motion from 
east to west. [ The earth, therefore, apparently moving 
in one direction exactly as fast as it actually moves in the 
opposite direction, consequently seems to an inhabitant 
of the moon to stand still' 2 in the heavens. 

335. These phenomena would only be seen by a spec- 
tator on the side of the moon nearest to us, for to those 
inhabiting the remote hemisphere the earth would never 
come into view. Their long nights of nearly 15 days du- 
ration would therefore be extremely dark, since the 
brightest heavenly bodies, whose light could dissipate 
the gloom, are Mars and Jupiter, which would afford no 
more illumination to the inhabitants of the moon than 
they do to us. 

336. Acceleration of the Moon's motion in her 
Orbit. The time occupied by the moon in revolving 
about the earth is now really less than it was centuries 
ago. This remarkable fact was discovered by Dr. Hal- 
ley, in the following manner. Knowing the periodic 
time of the moon, as computed from the observations of 
modern astronomers, he compared it with that, deduced 
from the Chaldean observations of eclipses at Babylon, 
in the years 719 and 720, before Christ ; and also with 
the periodic time obtained from observations made at 
Cairo, by Ebn Junis, an Arabian astronomer who flour- 
ished in the 10th century. 

1. The moon would present the same phenomenon to us if she completed a 
revolution in her orbit in a sidereal day, for she would then actually move 
as fast from west to east as she would apparently move from east to west on 
account of the rotation of the earth. Under these circumstances, she would 
seem not to move at all. 

2. Though the earth would have no progressive motion in the heavens, 
she would change her place a little on account of her librations, rocking to 
and fro to a small extent in a direction parallel to her equator (libratiin 
in longitude,) and also in a direction perpendicular to it (libration in 
latitude.) 

Would the earth have any apparent motion as seen from the moon ? Give the explana- 
tion ? Could these phenomena )e seen from every point of the moon's surface ? Why 
not? What is said respecting the nights that prevail throughout that hemisphere of the 
moon which is turned from us ? What is said in respect to The time now occupied by Ui« 
moon in revolving about the earth 7 



172 SOLAR SYSTEM. 

337. These comparisons showed, that the motion of 
the moon had been accelerated from the era of the Chal- 
dean observations to that of Ebn Junis, and also from 
his time to that of Dr. Halley. 

The investigations of the profound mathematician La 
Place, have proved the existence of this phenomenon 
beyond a doubt. 

The amount of this acceleration of the moon's motion 
is extremely small being only a little more than ten 
seconds (10") in every hundred years. 

338. This variation in the moon's velocity, was ai 
first accounted for, by supposing that the space through 
which she moved was filled with a fluid like air, which, 
by the resistance, it opposed to the mass of the moon, 
lessened her centrifugal force. The earth would conse 
quently draw the moon closer to herself thus diminish- 
ing the magnitude of her orbit and decreasing her peri- 
odic time. 1 

339. La Place, however, showed that this view was 
erroneous, and proved that this increase of motion 2 was 
caused by a gradual diminution in the eccentricity of 
the earth's orbit. Moreover, that this diminution will 
continue for ages, when it will cease, and then the eccen 
tricity will begin in turn to increase ; and that these 
alternate changes will continue while the solar system 
exists. The acceleration of the moon must therefore 
follow the same law. For ages the motion will grow 
swifter and swifter until the eccentricity of the earth's 
orbit begins to increase ; after that era the moon's motion 
will be gradually slower and slower ; until again, at the 
end of countless ages, the limit will be reached, and her 
speed once more accelerated. 

340. The Moon's path in space. Since the moon 
revolves about the earth, and at the same time about the 

1. The periodic time of the moon is the time occupied by this orb, in 
cempleting a revolution about the earth. 

2. The periodic time being decreased, the motion of the moon must be 
increased. 

Who discovered this fact ? In what manner ? Whose investigations clearly proved its 
txistence ? What is the rate of the acceleration 1 How was this phenomenon at first 
accounted for ? What did La Place prove ? 



ECLIPSES OF THE SUN AND MOON. 173 

sun, l moving along with the earth in its annual circuit, 
her path in space necessarily partakes of these two mo- 
tions. Being now inside of the earth's orbit, and now 
outside, the path she describes around the sun and 
earth is an epicycloidal curve, intersecting the orbit of 
the earth twice every lunar month, and every where 
concave towards the sun. The whole departure of the 
moon from the earth's orbit either way does not exceed 
one four hundredth part of the radius. Her path there- 
fore around the sun, does not sensibly deviate from the 
elliptical orbit of the earth. 

341. The moon in her motions is subject to numerous 
irregularities, the explanation of which has tasked the 
highest powers of the most gifted astronomers. 



CHAPTER 111. 

ECLIPSES OF THE SUN AND MOON. 



342. The eclipses of the sun and moon are among the 
most grand and sublime of the phenomena of the 
heavens. In all ages of the world, they have been 
viewed by the ignorant with wonder and awe ; while to 
the man of science they have ever been subjects of deep 
iuterest and profound study. 

LUNAR ECLIPSES. 

843. An eclipse of the moon is the partial or total obscu- 
ration of her light, when she passes into the shadow of the 
earth. The sun, earth, and moon, are then in nearly the 
same straight line with the earth between the other two 
bodies. If the moon were self-luminous, like the sun, a 

1. The moon is not borne along by the earth, around the sun, she would 
revolve about the latter, if the earth was annihilated. 

State what is said respecting the moon's path in space ? What in regard to her mo- 
tions ? Of what does Chapter III. treat! What is said respecting the eclipses of the sun 
and moon * What is an eclipse of the moon ? When it occurs, what are the relative 
positions of the sun, moon, and earth? 



174 SOLAR SYSTEM. 

lunar eclipse could never occur ; but shining as she (iocs 
by reflection from the sun, the interposition of the solid 
body of the earth, cuts off the solar light, and the por- 
tions of the moon that enter the earth's shadow appear 
dark to our view. A lunar eclipse can never happen 
except when the moon is full, for it is only at this time 
that the earth is between the sun and moon, and its 
shadow is extended in the direction of the latter. 

344. If the plane of the moon's orbit coincided exactly 
with the plane of the ecliptic, she would pass through 
the earth's shadow at every revolution, and a lunar 
eclipse would take place at every full moon. But as the 
former is inclined to the latter at an angle of about 5° 
(Art. 312,) the shadow of the earth may at one time pass 
above the full moon, and at another below it. The full 
moon must therefore take place within a certain dis- 
tance of one of her nodes, 1 that is, near the plane of the 
ecliptic, to make it possible for an eclipse 2 to occur. 

345. When the moon, at the full, has her centre ex- 
actly at her node, it is in the same straight line with the 
centres of the sun and earth, and she is placed centrally 
in the shadow of the earth. But it is not necessary that 
the moon should be precisely in this position in order that 
an eclipse may happen ; for since she possesses an appa- 
rent breadth of about 30', and the shadow of the earth 
extends on each side of the node, her disk may be ob- 
scured when she is within a short distance of this point. 

The calculations of astronomers accordingly show 
that an eclipse may happen when the moon at the full 
is not more than 12° 24 / distant from one of her nodes, 
and must happen if her distance does not exceed 9°. 

1. It will be remembered that the moon's nodes are those points in her 
orbit where the latter intersects with the plane of the ecliptic. They aro 
consequently at once in the plane of the moon's orbit, and in that of the 
earth's. 

2. Eclipses are so called from the Greek word tK'Xeiifjur meaning a "disap- 
pearance." 

If the moon was self-luminous would there be any lunar eclipses ? In what phase must 
the moon he when a lunar eclipse happens 1 If the plane of the ecliptic and that of the 
moon's orbit coincided, how often would lunar eclipses occur 1 Why do they not now 
take place every month ? Near what point must the full moon be to make it possible for 
an eclipse to happen ? Explain why it is not necessary for the moon to be exactly at one 
•f her nodes for this phenomenon to occur'? Statetlie limits within which a liiuuf 
eclipse may happen 1 Those within which it, mast hcppeul 



175 

346. When the moon is entirely obscured, the eclipse 
is called Mai ; when only a portion of the disk is con- 
cealed partial, and when the disk just touches the edge 
of the shadow, the phenomenon is termed an appulse. 

347. Of the Earth's shadow. Since the rays of 
light move in straight lines, the shadow of a globe illu- 
mined by one of greater size is conical, and the length 
of its shadow will depend upon the size and distance., of 
the illuminating body. For the greater the relative size 
and the less the distance the shorter will be the shadow, 
and the smaller the size and the greater the distance the 
longer the shadow. The sun being vastly greater in 
magnitude than the earth, the shadow of the latter is ac- 
cordingly conical. 1 (Fig. 61,) and though they never 
vary in size, yet as they vary in their distances from 
each other, the earth's shadow is changeable in length, 
being shortest when the sun is in perigee and longest when 
in apogee. 

348. It is by no means a difficult matter to determine 
the length of the shadow, and by the aid of Fig. 61, we 
will explain the manner in which the calculation is 
made. In this figure S represents the centre of the sun, 
E that of the earth, and AD and PL rays of light from 
the edges of the sun, touching the earth at D and L, and 
meeting at B. The lines BD and LB bound the 
shadow, SEB is a straight line drawn from the centre 
of the sun through that of the earth, to the extremity of 
the shadow, and EB is the length of the shadow. Our 
task is to find how many miles long EB is. 

349. We must first direct our attention to the trian- 
gle DEB. We know the extent of DE, for it is a radius 
of the earth, and is 3956.2 miles long ; moreover, EDB 
is a right angle ; for if a line (as ADB) touches the sur- 
iace of a sphere at any point, and a line (as DE) is 

1. Strictly speaking the shadow is not an exact cone, the base ot which 
is a circle. It would be a cone if the earth was a perfect sphere but being 
an ellipsoid the base of the shadow is an ellipse instead of a circle. 

When is an eclipse total? When partial? What is an appulse? What is the 
form of the shadow of a globe illumined by one of a greater size 1 What does the length 
©f the shadow depend upon ? What is the form of the shadow of the earth 1 Whea 
onf est ? When shortest ■? Can its length be calculated 1 

S* 



176 



SOLAR SYSTEM. 
FIG. 61. 




drawn from the centre of the sphere to that point, the 
iine drawn from the centre and the touching line 
always make a right angle with each other. Now join 
AE, and we thus form two angles ; viz., DAE which is 
the sun's horizontal parallax, (Art. 94,) and AES which is 
the surfs apparent semi-diameter. In geometrical language 
AES, is called the exterior angle of the triangle AEB, 
and is equal to the sum of the two angles ABE and BAE. 
The angle EBA, is therefore equal to the angle AES, 
diminished by the angle E AB ; or in other words equals 
the difference between the sun's apparent semi-diameter 
and his horizontal parallax. The value of the difference at 
the sun's mean distance is 15 / 51.4". Therefore, in the 
triangle DEB, since we know the value of all the angles 
and the length of one side, we proceed to select from 
the trigonometrical tables a similar triangle as D^B 1 , 
and institute a proportion as we have before shown 
between the sides. 

350. We thus find, that if the line B'E 1 represents 
one mile, D'E 1 consists of four thousand six hundred and 
twelve millionths of a mile ; and the proportion runs thus, 
D*E l (,004612ths of a mile) : B^ 1 (one mile) : : DE 
(3956.2 miles) : BE. Multiplying together the second 
and third terms of the proportion and dividing by the 
first, we obtain for the value of BE 857,806 miles. The 
mean or average length of the shadow is therefore about 
860,000 miles, extending beyond the earth's centre to a 
distance more than three and a half times that of the 

Explain how by Fig. 61. What is the mean length of the earth's shadow in miles'! 



OF THE PENUMBKA. 177 

moon from the earth. "When the sun is at the perigee, 
the length of the shadow is about 14,400 miles shorter, 
and when at the apogee, nearly 14,700 miles longer than 
the mean value. 

351. Extent of shadow tea versed by the Moon. 
It is proved by mathematical investigations, that the aver- 
age breadth of the earth's shadow where the moon crosses 
it, is about three times the diameter of the moon or nearly 
6,500 miles. But the length of the moon's path through 
the shadow is affected by two circumstances ; First, the 
varying distance of the sun from the earth ; Secondly, the 
varying distance of the moon from the earth. For when 
the sun is in apogee at the time of the eclipse, the breadth of 
the shadow, at the average distance where the moon 
crosses it, will be greater than usual; (Art. 350,) and if the 
moon then happens to be in perigee, she will cross the 
shadow about 13,000 miles nearer the earth than at her 
average distance of 240,000 miles, and will consequently 
traverse a broader part of the shadow. 1 

But if the reverse happens, the sun being in perigee, 
and the moon in apogee, the proximity of the sun will 
narrow the earth's shadow at the average distance where 
the moon crosses it, while the moon being now farthest 
from the earth, will pass through the shadow at a still 
narrower place, nearly 13,000 miles, beyond its average 
place of crossing. 

352. Of the Penumbra. On each side of the 
shadow of the earth there exists, to a certain limit, a 
space where there is a partial shadow or penumbra* 
Outside of this space the moon is illumined by the full 
orb of the sun, but as she enters the penumbra the dark 
body of the earth begins to interpose itself, and cuts off 
a portion of the sun's light. As she continues to ap- 

1. It will be remembered that the moon in apogee is 26,000 miles farther 
from the earth than when in perigee (Art. 310.) Her average distance 
will therefore differ from her apogee and perigee distances by 13,000 miles. 

2. See page 133, note 2. 

How does it compare in length with the moon's distance from the earth 1 When the 
»un is in peiigee, how much shorter is the shadow than its mean length 1 When the sun 
is in apogee how much longer 1 What is the average breadth of the earth's shadow where 
ne moon crosses it ? By what too circumstances is the length of the moon's patt through 
-De shadow affected 1 Explain why ? What is the penumhra 7 



178 SOLAR SYSTEM. 

proach the shadow, more and more light is intercepted , 
and at the moment the earth totally hides the sun from 
any part of the moon, that part at the same instant 
passes the inner limit of the penumbra and enters the 
shadow. 

353. The space occupied by the penumbra is deter- 
mined as follows : Eeferring to Fig. 61, and supposing 
the lines ALW and PDU, to be drawn, touching the 
earth at the points D and L, l the penumbra is found on 
each side of the shadow bounded by the lines UD, DB 
and BL, LW. QM represents the path of the moon, and 
the several small circles on the line QM, are different 
positions of the moon at and near the time of an eclipse. 

354. It is evident from the slightest glance, that the 
moon when nearest Q, is exposed to all the light of the 
solar disk ; but that as soon as she passes beyond the 
line LW, a portion of the sun near A, can not be seen 
from the moon, on account of the interposition of a por« 
tion of the earth at L. More and more of the sun's disk 
will become invisible at the moon as she advances 
towards the line LB, and when she has passed this line, 
the disk of the sun is entirely concealed from a part of her 
surface, if not from all, by the intervention of- the earth. 

355. The moon leaves the shadow, re-entering the pe- 
numbra on the opposite side, when she has crossed the 
line DB ; for here rays of solar light from the regions 
about A now shine upon her, and when she has passed 
the line DU, she emerges from all obscurity and the 
full light of the sun again illumines her surface. The 
space DBL therefore comprises the shadow of the earth, 
while the penumbra is limited as before stated, by the 
lines UD, DB and BL, LW. 

356. Duration of a Lunar Eclipse. When a total 
eclipse occurs, the moon, if she passes centrally through 
the shadow, may be completely obscured for the space 

1. The straight lines PU and AW do not touch the surface of the earth 
at exactly the same points where AB and PB touch ; viz., at D and L, 
but very near them. 

State what changes in illumination the moon undergoes, as she advances from beyond 
the penumbra into the shadow 1 Explain from figure. For what space of time is the 
vaoon obscured during a total eclipse, when she passes centrally through the shadow 1 



RED LIGHT OF THE DISK. 179 

ot about two hours, for she moves through a space equal 
to her own breadth in about an hour, and as the breadth 
of the earth's shadow where the moon crosses it is 
nearly three times her diameter, she must traverse two 
thirds of the breadth of the shadow in obscurity. 

357. The duration however of complete eclipse will de- 
pend upon the direction of the moon's transit through 
the shadow, and also upon the varying distances of the 
sun and moon from the earth, as explained in Art. 351. 
A lunar eclipse may continue for the space of about five 
and a half hours, counting from the moment the moon 
enters the penumbra, till the instant she leaves it. 

358. Ked light of the Disk. During a lunar eclipse 
the darkened surface of the moon is illumined by a red- 
dish light, a phenomenon resulting from the refraction of 
the solar rays by the earth's atmosphere. For the solar 
beams entering our atmosphere are refracted towards 
the earth, and • being thus herd into the shadow pass on- 
ward and strike the moon. Being thence reflected to 
us, they are still sufficiently bright to render her surface, 
even in shadow, distinctly visible. The color of the light 
is owing to the same cause that gives rise to the ruddy 
tints of sunset clouds ; the white light of the sun in 
struggling through the atmosphere loses its feebler rays, x 
while the red, which possesses the greatest power to 
overcome any resistance it encounters, emerges, and im- 
parts its own hue to the objects upon which it falls. 

This reddish light is of sufficient intensity, to enable 
observers to detect the obscure regions and spots on the 
lunar disk. The following facts are stated by Hind. 
During an eclipse of the moon that occurred on the 23d 
of July, 1823, M. Gambart saw all the lunar spots dis- 
tinctly revealed. In an eclipse that happened on the 

1. When a sunbeam is refracted, the seven colors of which it if com- 
posed ; to wit, red, orange, yellow, green, blue, indigo, and violet, aro 
turned out of the course of the original beam. The red deviating the least 
and the violet the most. The red is therefore least affected by the resist- 
ance it meets with. 

Why ? What does the duration of complete eclipse depend upon ? How long may a lunar 
jclipse last, counting from the time the moon enters to the time she leaves the penumhra ? 
What phenomenon occurs during a lunar eclipse? How is it caused? To what is the 
color owing? What can be discerned on the disk of the moon by means of this light? 



180 SOLAR SYSTEM. 

26th of December, 1838, Sir John Herschel observed, 
that the moon was clearly visible to the naked eye, 
when completely immersed in the earth's shadow ; gleam- 
ing with a swarthy copper hue, which changed to bluish 
green at the edges, as the eclipse passed away. Similar 
phenomena were noted during the total lunar eclipse 
of March 8th, 1848. 

The spots on the surface, even at the middle of the 
eclipse were distinctly seen by many observers, and the 
general color of the moon was a full glowing red. So 
clearly did the lunar dish stand forth to view, that many 
of the observers doubted if there was any eclipse at all. 

359. Earliest observations of Lunar Eclipses. 
Observations were made on lunar eclipses at Babylon, 
by the Chaldeans, in the years 719 and 720 B.C. They 
relate to three eclipses, and are the earliest observations 
of this kind, in the annals of science. The first eclipse 
occurred on the 19th of March, 720 B.C., and was total 
at Babylon. The second happened on the 8th of March, 
719 B.C., and the third, on the 1st of September in the 
same year ; both were partial eclipses. 

ECLIPSES 0E THE SUN. 

360. An eclipse of the sun takes place when the moon 
m her revolution about the earth, comes between the earth 
and the sun, and casts her shadow upon the former ; 
concealing from our view, by her interposition, either a 
part or the whole of the bright disk of the sun. A solar 
eclipse can therefore only occur at the time of new moon 
or conjunction ; and as in the case of lunar eclipses, it 
would happen every revolution, if the plane of the ecliptic 
coincided with that of the moon's orbit. But this is not 
the fact, and a solar eclipse can therefore only take place 
when at new moon the lunar orb is at or near one of her 
nodes. The greatest possible distance of the moon from the 
node at which a solar eclipse can occur is 18° 36'. 

361. Form of the Eclipse. A solar eclipse may be 

Detail the facts mentioned by Hind 1 Give an account of the earliest observations of 
lunar eclipses? What is the cause of a solar eclipse ? At what phase of the moon caK 
it only occur 1 Whv not at every new moon 1 Where must the new moon occur 1 
What is the greatest possible distance from the node that a solar eclipse can take place 1 



SHADOW OF THE MOON 181 

'partial, total, or annular. It is partial when only a por- 
tion of the dark body of the moon interposes between 
the snn and a spectator upon the earth. Total, when the 
apparent diameter of the moon exceeds that of the sun, 
and the former body passes nearly centrally across the 
solar disk. Annular, when the moon passes in like 
manner nearly centrally before the sun, but her apparent 
diameter is less than the solar ; the entire body of the sun 
being then obscured with the exception of a brilliant ring, 
around the borders of the moon. When in this case the 
centres of the sun, moon, and earth are exactly in the 
same straight line, the eclipse is termed annular and cen' 
tral, and the bright ring possesses a uniform breadth. 

362. Shadow of the Moon. The distance of the 
moon from the sun is subject to variation, and this cir 
cumstance affects the length of the moon's shadow. The 
farther this orb is from the sun the longer will be her 
shadow, and the nearer the shorter. Now when, during a 
solar eclipse, the earth is nearest to the sun, and the moon 
is farthest from the earth, the lunar shadow will be the 
shortest ; but when the earth is farthest from the sun, and 
the moon is nearest to the earth, it will be the longest. 
That such must be the case is evident ; for in the first in- 
stance the orbitual motions of the earth and moon bring 
the latter as near as possible to the sun, and in the second, 
remove her as far as possible from this luminary. In as- 
tronomical language the lunar shadow is therefore short- 
est, when the earth is at her perihelion and the moon in 
apogee, and longest, when the earth is at her aphelion and 
the moon in perigee. 

363. The average length of the moon's shadow is found 
to be about equal to her mean distance from the earth. 
It will accordingly, for the reasons above assigned, at 
times fall short of the earth, while at others it will be so 
much extended, that a shadow of considerable breadth 
passes over the surface of the globe. 

364. When the shadow does not reach the earth, it is 

What is stated respecting the form of a solar eclipse "? When is it partial? When 
total ? When annular ? When annular and central ? State the cause of the variations 
in the length of the moon's shadow? When is it shortest ? When longest? Give the 
•ame statements in astronomical language ? To what is the average length of the moon's 
thadow nearly equal 1 What happens if it is less or greater than the mean length 1 



182 



SOLAR SYSTEM. 



manifest no total eclipse can occur ; although the sun, 
moon, and earth are so situated in every other respect 
as to give rise to this phenomenon. When it does reach 
the earth, the space that it covers on the surface of the 
latter, will depend upon the position of the end of the 
shadow in reference to the surface of the earth. If the 
end of the shadow just touches the earth, there will be 
a total eclipse only at the place it touches. But if the 
point where the shadow would terminate, if the earth 
did not interpose, is situated, as at F in Fig. 62, far on the 
other side of the earth, then the eclipse will be visible 
throughout a region of considerable extent. The largest 
extent of surface on the earth, covered at once by the 
shadow of the moon is about 180 miles in diameter. 

365. The lunar shadow like that of the earth, has also 
its penumbra, which partially obscures our globe. The 
greatest breadth of terrestrial surface enclosed by the 
penumbra is nearly 5,000 miles. 

366. In Fig. 62, this subject is illustrated, S here rep- 



FIG. 62 




SOLAR ECLIPSE. 



resents the sun, M the moon, and E the earth. The 
form of the shadow is defined by the lines CF and DF, 
a portion of the shadow is however cut off by the inter- 
position of the earth. The breadth of the shadow on the 
earth is represented by the distance from to P, and 
the breadth of the penumbra on each side of the shadow, 
by the curved lines GO and PH. 

367. Altitude of the Moon — Its effect on Eclip- 
ses. Since the moon is nearer to the surface of the earth 
whe*n in the zenith than when upon the horizon, by about 

When will no total eclipse occur ? Upon what does the extent of terrestrial surface 
covered by the shadow depend 1 Give the two illustrations ? What is the greatest 
extent of surface obscured by tho shadow? State what is said respecting the pen 
umbra and its breadth ? 



ALTITUDE OF THE MOON. 183 

4,000 miles, it may happen that a total eclipse takes 
nlace in one part of the world, and not in another. Two 
places may be so situated that the moon is on the horizon 
at one station and 'in the zenith at the other, when a solar 
eclipse is about to happen. Now it is possible that the 
lunar shadow may fall just short of the place where the 
moon appears upon the horizon, but as the other station 
is nearer to the moon by about 4,000 miles, the shadow 
may reach the latter place, and the sun will consequently 
for a short time be there totally eclipsed. 

368. This phenomenon is illustrated by Fig. 63. 



FIG. 63. 




AiTlTUDE OF THE MOON ITS EFFECT ON ECLIPSES. 

Here ZBHE represents the earth, OR the moon's orbit, 
M and M l two positions of the moon, and S, S 1 her 
shadow. To a spectator at H, the moon M is on the hori- 
ion, and there is no total eclipse, for the shadow does 
not reach him, but when the moon in her orbitual mo- 
tion is at M 1 she is in the zenith to a spectator at Z, and 
rhe shadow reaches him causing a total eclipse, 1 though 

1. The distance between the centres of the moon in the two positions 
M and M 1 is equal to the distance between the extremities of S, S 1 , 
i.e., to the radius of the earth, or about 4,000 miles. By dividing the 
length of the moon's orbit by the time of her revolution, we obtain her 
velocity, which is more than 2,000 miles per hour. The moon therefore 
moves from M to M 1 in less than two hours, and the shadow is likewise 
:arried from S to S 1 in the same time. 



Explain how the altitude of the moon modifies eclipses ? Explain from Figure 



184 SOLAR SYSTEM. 

the shadow is of the same length as when the moon was 
at M. 

369. For the reason just given an eclipse which would 
be annular to a person beholding the moon upon the 
horizon might be total to one observing her at the 
zenith. 

370. Total Eclipse of the Sun. We have re- 
marked that eclipses of the sun and moon are among the 
grandest phenomena in nature, but no form of eclipse 
is so impressively sublime as a total eclipse of the sun. 
The gradual withdrawal of the solar light, and at length 
its total extinction ; the oppressive and unnatural gloom 
that overspreads the earth, so different from the obscu- 
rity of night, and the appearance of the stars, at such an 
unusual time, all imp* ess the mind with a deep solem- 
nity. It is not surprising that a spectacle of this kind 
has ever filled barbarous and even civilized nations with 
astonishment and dread, as though they were on the 
brink of some awful calamity. 1 But eclipses whether 
total or otherwise are the source of one of the noblest 
triumphs of science ; for astronomers are now so well 
acquainted with the Jaws, that regulate the motions of 
the heavenly bodies, that the very minute of an eclipse 
can be predicted centuries before it occurs, and the dates 
of events which happened thousands of years ago, can be 
unerringly fixed, by retrograde calculations of these 
phenomena. 2 

1. A total eclipse of the sun occurred during the war between the Medes 
and Lydians, related by Herodotus. In the midst of a battle, the sun was 
blotted out from the sight of the contending armies, and so great was their 
terror at such a strange event that they threw down the weapons, and made 
a peace upon the spot. This eclipse is said to have been predicted by 
Thales. 

2. When Agathocles, the tyrant of Syracuse, invaded Africa, for the 
purpose of attacking the Carthagenians in their own country, a total eclipse 
of the sun occurred at the time the expedition was setting sail. This cir- 
cumstance disheartened the soldiers, but Agathocles revived their courage 
by representing that this event portended the defeat and ruin of their ene- 
mies. This eclipse occurred according to retrograde calculations on the 1 5th 
of August, 310 B.C. An eciipse of the sun also happened at the very time 
Xerxes set out from Sardis, to invade Greece. The eclipse proves that this 

May an annular eclipse in one part of the world be total in another 1 What is said in re- 
•pect to a total eclipse of the sun 1 How have they been regarded by barbarous and even 
civilized nations ? What have they pro\ei u> astronomers 7 



TOTAL ECLIPSE OP THE SUN. 185 

371. During a total eclipse of the sun, many singular 
appearances are usually observed. At the moment the 
bright edge of the sun is just disappearing or appearing, 
it is often seen broken up into a series of luminous 
points known by the name of Baily's beads, from Sir 
Francis Baily, who first observed them. This phe- 
nomenon has been supposed to be caused by the lunar 
mountains which intercept the sun's light that streams 
through the intervening valleys. 

When the sun is completely hidden, a beautiful ring 
or corona 1 of light appears around the dark body of the 
moon. In the eclipse of 1842, one observer describes 
it as a ring- of peach-colored light, another as white, and 
a third as beaming with a yellowish hue. During the 
total eclipse of the sun, August 7th, 1869, the corona 
seemed to be composed of four or five prominent por- 
tions, and in no instance exceeding in height one-sixth 
of the sun's diameter. The breadth of the corona, no- 
ticed by Mr. Bond, during the eclipse of July 28, 1851, 
was about one-half of the sun's diameter. 

372. But the most brilliant phenomena remain to be 
described. When the sun is completely concealed, and 
the corona is displayed, rose colored flames appear to 
dart out from the edge of the moon, emanating from 
the bright ground of the corona, and so distinct that 
they are frequently visible without the aid 'of a tele- 
scope. During the eclipse of July 28th, 1851, Prof. 
Bond of Cambridge, noticed these beautiful rose colored 
flames, two of which were connected by an arch of light, 
resembling a rainbow. They appeared also in great 
splendor at Des Moines, Iowa, during the eclipse of 
1869. They have already been described and their 
nature explained in Art. 258. 

373. Fig. 64 represents this eclipse as seen by Mr. J. 

historical event occurred on the 1 9th of April, 481 B.C. A lunar eclipse 
which happened on the 21st of September, 331 B.C., fixes the date of 
the battle of Arbela, in which Alexander triumphed over Darius, king 
of Persia. The eclipse occurred 11 days before the victory. 
1. Corona, a Latin word signifying a crown. 

Describe the various appearances that are beheld during a total eclipse of the sun ? 
What appearances were observed by Mr. Bond, during the eclipse of July 28, 1851? 



186 



SOLAR SYSTEM. 



R. Hind, in Sweden. The eclipsed sun is here seen sur- 
rounded by a corona, the whiter portions of which near 



FIG. 64 




TOTAL ECLIPSE OF THE SUN, AS SEEN BY MR. J. R. HIND, NEAR ENGELHOLM, 
IN SWEDEN, JULY 28, 1851. 

the dark circle indicate the positions of the jets of flame 
and the arch of light 

374. Duration of a Solar Eclipse. No eclipse of 
the sun can last longer than six hours. The duration of 
a total eclipse never exceeds eight minutes, nor that of an 
annular twelve and a half minutes. 

375. Solar and Lunar Eclipses — Points of dif- 
ference. When a lunar eclipse occurs, it can be seen 
from every part of that side of the earth, which is turned 
towards the moon. For this hemisphere is necessarily in 
the earth's shadow, and a spectator here situated be- 
holds the moon eclipsed when she enters the shadow. 

Describe Fig. 64. How long can any eclipse of the sun last 1 How long a total 7 How 
long an annular eclipse 1 



QUANTITY OF AN ECLIPSE. 187 

376. In the case of a solar eclipse, the shadow of the 
moon passes across the earth in less than four hours, 
(Art. 368 note 1,) and an eclipse can only occur in the 
path of the moon's shadow. Every part of the terrestrial 
hemisphere turned toward the sun will not therefore be 
eclipsed, but only those portions that are traversed by 
the lunar shadow. 

The extent and path of the shadow must accordingly 
be determined before we can know in what regions of 
the earth the sun will be eclipsed. 

377. These differences in respect to lunar and solar 
eclipses, arise from the different positions of the observer 
in the two cases. During a lunar eclipse he is on the 
body that/or7ns the shadow, during a solar eclipse he is 
on the body that receives the shadow. 

378. Frequency of Eclipses. Seven is the greatest 
number of eclipses that can occur in the course of a year, 
and two the least. If seven take place five may be solar 
and two lunar or three may be eclipses of the sun and 
four of the moon. Six eclipses in a year is an unusual 
number, four the average and two the hast ; in the last 
case the eclipses will be solar. 

379. An eclipse of the moon sometimes happens the 
next full moon Sifter an eclipse of the sun, and the reasons 
are as follows. The solar eclipse taking place at or near 
one of the moon's nodes, the shadow of the earth extends at 
this time across the moon's orbit, and is at or near the other 
node. Now the moon's orbitual motion is so rapid that 
after causing the solar eclipse, she may sweep round to 
the other node, before the earth's shadow has departed so 
far from it, as to be out of the moon's way. Under 
these circumstances she enters the shadow and a lunar 
eclipse occurs. 

380. Quantity of an Eclipse. The quantity of an 
eclipse, is the extent of the obscuration of the eclipsed 
body, and is estimated in the following manner. In a 

State in what respects solar and lunar eclipses differ ? How do these differences arise 1 
What is the greatest number of eclipses that can occur in a year ? What the least ? If 
seven take place what will be the number of solar eclipses, and what the number of lunar ? 
What is an unusual number in a year 1 What the average ? What the least number 1 
[f only two occur, are they solar or lunar? Explain why an eclipse of the moon may 
happen the next full moon after a solar eclipse ? What is the quantity of an eclipse 7 



188 SOLAR SYSTEM. 

lunar eclipse, for example, the diameter of the moon ia 
supposed to be divided into 12 equal parts, called digits, 
and the number of such parts that lie within the earth's 
shadow, at the time the moon's centre is nearest to the 
centre of the shadow, determines the quantity of the eclipse. 
"When the moon is entirely immersed in the shadow, as 
in the case of a total eclipse, the quantity is found in like 
manner, by supposing a line to be drawn from the centre 
of the shadow to its outer edge through the centre of the 
moon, and then dividing the part included between the 
inner edge of the moon, and the outer edge of the shadow, 
by one twelfth part of the moon's diameter. 

This subject is illustrated in Fig. 65, where M repre- 

FIG. 65. 




sents the moon, N one of her nodes, NMP a portion of 
the moon's orbit, and NSCE the direction of the plane of 
the earth's orbit. The circle EOSK is a section of the 
earth's shadow, which completely envelopes the moon, 
causing a total eclipse : the line OC is a radius of the 
circle EOSK and passes through the centre of the moon. 
The quantity of the eclipse is obtained by dividing the 
line LO by one twelfth part of DL the moon's diameter. 
If the eclipse instead of being total had been partial, 
and the moon's centre M, had been at the point O, then 

What is meant by the term digit? How is the quantity of nn eclipse esfimuted 1 
How is the quantity found in a total eclipse 1 Explain from Figure. 



THE PERIOD OF THE ECLIPSES — THE SAROS. 189 

one half of her diameter ML would have been in shadow, 
and the quantity of the eclipse would have been six 
digits. 

381. The period of the Eclipses — The Saros. 
It was discovered by astronomers centuries ago, that if 
the eclipses that happen during a period of about 18 
years, are noted in their order, that the series is repeated 
during the next period in nearly the same manner as 
before. 

The reason of this will be evident from the following 
considerations. 

382. We have seen that eclipses depend upon the 
nearness of the moon to her node when new and full 
But the node is in motion around the ecliptic, retrograd 
ing at the annual rate of about nineteen and a half de 
grees, 1 while the moon is also in motion around the earth 
Now an inquiry may reasonably be made whether, sup 
posing that an eclipse was to take place to-day exactly 
at one of the moon's nodes, in which case, the sun and 
the moon would be in the line of the nodes, there might not 
be such a relation between the motion of the moon and 
the motion of the node, that after a certain interval of time 
another eclipse would again occur at the same node ; so 
that the moon and the sun during the next succeeding 
interval would go through the same series of positions 
in respect to each other as during the first, and re- 
produce the same set of eclipses, resulting from these 
positions. 

383. Such a relation is found to exist very nearly 
For if there was to-day a solar eclipse, the sun and moon 
as seen from the earth, being exactly at one of the moon's 
nodes, the moon would be there again in s 29.53 days (a 
synodical month, Art. 275,) and the earth in its revolu- 
tion about the sun, would bring the same node again to 
the sun in 346.62 days, a period which is termed the 

1. The daily retrogadation is 3' 10" (Art. 315,) which gives about lOp 
for the annual rate. 

2. This is the expression for the length of a lunar month in days and 
the decimals of a day. More nearly 29.5305887. 

State what is said respecting the period of the eclipses ? Explain in full the muse o» 
this recurrence of a series of eclipses? 



190 



SOLAR SYSTEM. 



synodical revolution of the moon's nodes. ! Now if 29.53 
was precisely contained in 846.62, at the end of this time 
the sun and moon would be again at the same node, and 
the same set of eclipses would recur at intervals of 346.62 
days. This however is not the case, since 29.53 is not 
exactly contained in 346.62, but if we multiply 29.53 
by 223 and 346.62 by 19, the products will be respec- 
tively 6585.32 and 6585.78. 223 synodical months are 
therefore almost equal in length to 19 synodical revolu- 
tions of the node. If therefore an eclipse happens on any 
day when the sun and the moon are exactly in the line 
of the lunar nodes, the two bodies will be again precisely 
in the same position, within less than half a days time, 
after a period of about 6585 i days, or nearly 18 years 
and 11 days. At intervals therefore of 18 years and 11 
days eclipses recur in nearly the same order. 

384. This period, obtained by observation indepen- 
dently of theory, is supposed to have been known to 
the Chaldeans under the name of Saros, and that it was 
employed by them to predict eclipses : within it there 
usually occur 70 eclipses, 29 lunar, and 41 solar 



CHAPTER IV, 



CENTRAL FORCES AND GRAVITATION. 

385. "We have shown in the preceding pages, that the 
earth revolves about the sun, and that the moon in like 



1. The earth in her annual revolution completes the circuit of the eclip- 
tic, or 360° in about 365 days, advancing from west to east at the daily rate 
of nearly lo, but the lunar nodes retrograde from east to west at the yearly 
rate of nearly 19^°. If therefore to-day one of the nodes coincided in posi- 
tion with the sun as seen from the earth, this coincidence would next occur 
when the earth lacked about 19|° of completing her annual circuit, and as 
the moves in her orbit about 1° a day, the interval of time between these 
two coincidences is nearly 346.62 days, more accurately 346,619,851. 

What is meant by a synodical revolution of the moon's nodes? What is the length <•( 
the period of the eclipses ? What ancient astronomers tire supposed to have employed 
•-his period in the prediction of these phenomena? What did they call it? How many 
eclipses usually happen within this period? How many of these are lunar 1 How many 
s»lar ? What is the subject of Chapter IV. ? 



CENTRAL FORCES AND GRAVITATION. 191 

manner, describes an orbit around the earth. All the 
other members of the solar system have also their re- 
spective orbits, and possibly the sun itself, with its attend- 
ant planets and comets, revolves around some vast central 
body in the depths of space. 

386. In view of these facts an interesting suggestion 
arises ; viz., what Are the forces which cause one 

UEAVENLY BODY TO REVOLVE ABOUT ANOTHER? 

This point we will now investigate before we proceed 
farther in the discussion of the solar system. 

387. When a body revolves about another as its cen- 
tre, we find that it is influenced by two forces, one of 
which tends to make it fly away from the central body, 
and the other to approach it. The former is termed the 
centrifugal 1 force, the latter the centripetal. 2 

388. If a person fastens a bullei to one end of a string, 
and then holding the other in his hand whirls the bullet 
around, it describes its circular path under the action of 
the two kinds of forces just mentioned. If the string 
were suddenly cut while the bullet was revolving, the 
latter would speed away from the centre of its orbit (the 
hand) like a stone from a sling. The force which thus 
actuates it, is its centrifugal force. Now when the string 
was whole, the bullet was prevented from obeying this 
centrifugal force, and kept in its circular path by the 
resistance of the string, which virtually drew the bullet 
towards the centre of its orbit, with the same power 
that the centrifugal force then tended to draw it away. 
The tension of the string is therefore the centripetal 
force. 

389. Let us advance one step further. We can 
imagine that the hand of the person instead of being 
connected with the bullet by any material bond as a 
string, draws the bullet towards it by an attractive power 
that resides within it, just as a magnet draws to itself 

1. Centrifugal from the Latin, centrum, a centre and fugere to fleu 
away. 

2. Centripetal from the Latin centrum, a centre and petere to seek. 

What has been shown in the preceding pages ? What inquiry arises in view of the*, 
facts 1 When a body revolves about another as its centre, how many forces totur .e it* 
What are they called ? Give the illustration 1 Which is }-ere th* ct*t*if gnl % and 
which the centripetal fotcJ 1 What can we next imagine ? 



192 SOLAR SYSTEM. 

any particles of iron that are near it. We can moreove 
suppose, that the attractive power is so adjusted k 
amount to the centrifugal force that it exactly counteract* 
the effort of the latter to make the bullet deviate from a 
circular path. Under these circumstances, the com* 
bined influences of the centrifugal and attractive forces, 
would cause the bullet to revolve in a circular path 
around the hand of the experimenter, without the in- 
tervention of a string. 

390. Now a heavenly body revolves about its central 
orb, by the action of centrifugal and centripetal forces, 
like the bullet in the preceding illustration. But no 
solid substance, no material chain or rod connects the 
earth or any other planet with the sun, restraining its 
centrifugal force, and keeping it in its path in its cease- 
less circuits, around this mighty orb. What then is the 
nature of the centripetal force, which causes a heavenly 
body to move with unerring precision in its orbit? 
Does there actually exist in the central body as we have 
imagined an attractive power, which constitutes the centri- 
petal force ? Let us see if this is the case. 

39L Of Gravity. When a body falls from rest 
towards the ground it descends in a straight line in the 
direction of the centre of the earth, under the influence 
of what is termed the force of gravity. 

There accordingly resides in the earth a power, which 
tends to draw other bodies towards its centre : in other 
words a centripetal force. 

392. We recognize its action in the paths described 
by projectile 1 bodies, for when a cannon ball is fired 
into the air, if it was influenced by no other force than 
that of projection, it would continue forever to speed 
away from the earth, in a straight course. But owing to 
the action of gravity the body is drawn to the earth, de- 

I . By projectile bodies is here meant those which are impelled forward 
vy force through the air. This force is called the projectile force. 

What may we suppose to be the relations of the attractive and centrifugnl forces to each 1 
How would the bullet then move without the aid of the string? What forces cuuse a 
heavenly body to revolve around its central orb ? What inquiries are here mnde ? When 
a body falls from rest what direction does it take '! What is that force termed which 
causes it to descend towards the earth ? What kind of power then resides in the earth ? 
In what do we recognize its action.' If the projectile force alone existed, what wouH be 
the path of the body? In consequence of gravity what i.s its path ? 



GRAVITY — ITS VARIATION. 193 

scending to it in a curved path, concave towards its 
surface. 

393. The greater the projectile force the greater will be 
the space passed over by the body before it reaches the 
ground ; and we may imagine the impulse to be so pow- 
erful as to carry the body completely around the earth 
to the point from whence it started. In this case, the 
projectile force remaining the same, the body would 
recommence its circuit and continue to revolve around 
the earth like the moon. 

394. Its Variation. The force of gravity above the 
surface of the earth, varies inversely as the square of the 
distance from the eartKs centre. By this expression we 
mean that if gravity exerts at the surface of the earth 
for instance, or about 4,000 miles from the centre a cer- 
tain power, it will exert at twice this distance from the 
centre, or 8,000 miles, only one fourth of this power. 
Thus, at the surface of the earth, a body descends freely 
under the action of gravity 16 T \th feet per second, but at 
the distance of 8,000 miles from the earth's centre, it 
will fall through only one fourth of this space in a second, 
or 4: i\th feet 

395. This law is illustrated in Fig. 66, where A rep- 
resents the centre of the earth, BCDE a square portion 
of its surface, and BA, CA, DA, and EA the lines of di- 
rection in which gravity acts. Suppose these lines are ex- 
tended to F, Gr, H, and I, and the square FGrHI is formed, 
whose distance from A is twice that of the square BCDE. 
Now it is manifest that the amount of gravity which is 
contained in the first square BCDE is the same as that 
which is contained in the second square FGrHI, but its 
intensity or strength in the latter is as much less than that in 
former, as the square FGHI is greater than BCDE. But 
FGrHI contains four small squares each equal to BCDE, 
therefore, the intensity of the force of gravity at F, 
which is twice as far from the centre as B, is one fourth 
of what it is at B. If we construct another figure 
JKLM at four times the distance of B from A, it will 

If the projectile force "is increased, what is true in regard to the extent of space passed 
•ver by the body ? If the impulse was so great that the body passed round the earth to the 
place where it started, what would happen ? According to what law does gravity varv 1 
What is meant by this expression ? Explain from Figure. 



194 



SOLAR SYSTEM. 



FIG. 66. 




1HE FORCE OF GRAVITY VARIES INVERSELY AS THE SQUARE OF THE DISTANCE. 



contain sixteen squares each equal to BCDE, and the 
force of gravity will here be diminished sixteen times ; all 
which accords with the rule just stated. 

396. The change in distance must be great, for the 
variations in the force of gravity to be appreciable. It 
is therefore regarded as a constant force at every part 
of the earth's surface, for the difference in the distances 
from the earth's centre, at the sea level and upon che 
loftiest accessible heights is too small to cause any ma- 
terial variation in the force of gravity. 

397. In the beginning of the 17th century, Kepler 
discovered by his unconquerable energy of mind, those 
famous laws which still bear his name, (Art. 193,) one 
of which announces that the planets revolve in elliptical 
orbits around the sun, which occupies a common focus. 

But though his perseverance was crowned with such 
success, he knew not the controlling force which holds 
the planets to the sun, and keeps them in their orbits. 
The glory of this discovery was reserved for another 
whose genius has illumined the whole field of science. 

398. Universal Gravitation discovered. In the 
year 1666, when the plague made such fearful ravages 
in England, the illustrious Newton retired from Cam- 
bridge, where the pestilence then raged, to his country 
house at Woolsthorpe. While sitting one day alone in 
his garden, the fall of an apple led him to reflect upon 
the nature of terrestrial gravity. He already knew that 

Are the variations in the force of gravity perceptible when the differences in the dis- 
tances are small ? Where is gravity regarded as a constant force, and why 1 When did 
Kepler discover those laws which bear his name 1 Did he ascertain what that force ii 
>vhich control the motions of the planets? 



UNIVERSAL GRAVITATION DISCOVERED. 195 

it caused the path of a projectile to be curved toward 
the earth, and that it was as sensibly powerful upon 
the tops of lofty mountains as at the sea level ; and 
he conceived that if it existed on the highest points 
of the globe without any perceptible diminution, it 
might possibly extend much farther, and that, possi- 
bly, the moon and planets were kept in their orbits by 
this power. He was next led to determine the value 
of the centripetal force which retains a body in a cir- 
cular orbit, and found that it could be expressed in 
terms of the periodic time of the body and of its dis- 
tance from the centre. 

399. From the third law of Kepler, viz : that the 
squares of the periodic times of the planets are as the 
cubes of their distances from the sun, he then inferred 
that this binding force varied inversely as the square of 
the distance from the centre of the attracting body. 

400. With these views the astronomer now proceeded 
to investigate the orbitual motion of the moon, by com- 
paring the space, which a body falls through in one 
second of time, at the earth's surface, with the space that 
the moon would be drawn towards the earth in the 
same time, under the action of gravity ; diminished in 
the inverse ratio of the square of the moon's distance 
from the earth's centre. 

401. This calculation was not at first satisfactory, 
because the correct length of the earth's diameter was 
not then known. Sixteen years afterwards when the 
true length was ascertained, Newton repeated his com- 
putation, and now his most sanguine hopes were fully 
realized. The force of terrestrial gravity diminished in 
the inverse ratio of the square of the moon's distance, 
from the earth's centre, was proved to be the very force 
that keeps this luminary in her orbit. 

402. The method of investigation pursued was the fol- 
lowing : The moon, starting from any point in her orbit, 
would move away from the earth in a straight line, if 

Relate the manner in which Newton was led to the discovery that gravity extended to 
the moon 1 How did the astronomer proceed to investigate the moon's orbitual motion ? 
Was the calculation at first satisfactory 1 Did it afterwards orove so 7 



196 SOLAR SYSTEM. 

some centripetal force did not deflect her, and cause her 
to move in a curve. 

The amount of this deflection is therefore a measure oj 
the centripetal force, and when we know the moon's dis- 
tance from the earth we can calculate the amount of this 
deflection for any given time, as one second; in other 
words through what extent of space the moon descends 
toward the earth in one second. Having ascertained this 
point, we next proceed to inquire if this unknown force 
is the force of gravity. 

403. Gravity at the earth's surface, causes a body to 
fall freely through a space of lGy^th feet in one second, 
as before stated, but the moon is removed 60 times far- 
ther from the centre of the earth than is the surface of the 
latter. Therefore, if gravity extends to the moon its force 
will be 3,600 (60 x 60) times less than it is at the earth's 
surface, and the space a body would fall through at the 
moon under its influence, during one second, would be 
found by dividing l^y^th feet by 3,600. The quotient 
thus obtained is .052 inches, a result identical with the 
computed amount of deflection. It is therefore inferred 
that the centripetal force which causes the moon to 
revolve about the earth is the force of gravity. 

404. The path of research opened by this grand dis- 
covery was not neglected. Succeeding researches have 
proved that the influence of gravity extends to all the 
bodies of the solar system, and even to the fixed stars. 
Every portion of matter whether large or small, a world 
or a grain of sand, is found to possess this attractive force 
and to be under its control. One body attracts another 
and is itself in turn attracted by it, the earth gravitates 
towards the sun, and the sun towards the earth ; the 
amount of attraction exerted by any body, being propor- 
tioned to the quantity of matter contained in that body. 

405. The investigations of astronomers, tend to show 
that gravity is coextensive with the material universe, and 
in view of its boundless diffusion, it has received a new 
appellation, being termed universal gravitation; A power 

Detail the mode of investigation ? Through what space will a body fall in one second 
at the distance of the moon from the centre of the earth 1 Does gravity extend in its in- 
fluence beyond the moon 1 What do we now know respecting it 7 What is it termed in 
in view of its wide ditfusion? 



THE PLANETS. 197 

OT VIKTUE OF WHICH ALL BODIES MUTUALLY ATTRACT 
EACH OTHER IN THE DIRECT RATIO OF THEIR QUANTITIES 
OF MATTER, AND IN THE INVERSE RATIO OF THE SQUARES 
OF THEIR DISTANCES FROM EACH OTHER. 

406. In addition to what has already been stated, this 
great principle accounts for the spherical form of the 
heavenly bodies, for nutation, the precession of the equi- 
noxes, the change in the obliquity of the ecliptic, the com- 
plex lunar motions, and various other celestial phenom- 
ena of which we shall hereafter speak. 



CHAPTER V, 



THE PLANETS. 



407. The planets are those heavenly orbs that re- 
volve directly about the 1 sun, from west to east, and shine 
by its reflected light. They have received this appella- 
tion, as we have stated, (Art. 2, note 1,) from the fact 
that they are seen moving among the tixed stars, and are 
constantly changing their places in the heavens. 

408. Mercury, Venus, Mars, Jupiter, and Saturn, 
have been known from the earliest ages ; for they are 
visible to the naked eye, and all but Mercury conspic- 
uously so. The rest of the planets, excluding the 
Earth, are recent discoveries ; all of these having been 
found since the year 1780, and 106 of them within 
the last 25 years. 

409. Many of the planets are attended by moons like 
the earth. The earth, as we know, has one moon, Jupi- 
ter four, Saturn eight, Uranus six, and Neptune one. 

1. The planetary bodies that revolve directly about the sun are called 
primary planets. Moons are termed secondary planets. The body about 
which another directly revolves is denominated its primary, thus, the sun 
is the primary of the earth, and the earth the primary of the moon. 

What is universal gravitation ? What is further said of this great principle ? What 
are planets ? Why are they so called ? Which have been known from a high anti- 
quity ? How many have been discovered since the year 1780 ? How many within 
the last 25 years? 



198 



SOLAR SYSTEM. 



Up to the present time, (1870,) the known number of 
planets, including the Earth, is 118, and of moons 20. 
There doubtless exist other planetary bodies in our 
system yet undiscovered, if we can infer anything from 
the harvest of planets that has lately rewarded the 
searching labors of zealous astronomers. 

410. The principal elements of the planets are given 
in the following table. In the computation of the dis- 
tances, the solar parallax is taken at 8.9", and the 
mean radius of the earth at 3,956.2 





TABLE OF ELEMENTS. 




Mean Polar 

Distances. 

Miles. 


Diame- 
ters in 
Miles. 


Periodic Time. 


Interior Planets. 








Mercury, ... 
Venus, - 

Earth, .... 
Mars, ... 


35,491,193 

66,318,330 
91,681,820 
139,700,160 


3,055 
7, .05 
7,912.4 
4,354 


87.969 days, or about | of ayr. 
224.701 " " 6-10 of ayr. 
385.256 " « 1 a ear. 
686.980 " " 2 " 


Asteroids, (av. distance,) 


244,798,469 




average period, 4] " 


Exterior Planets. 








Jupiter, - 
Saturn, - 
Uranus, - 
Neptune, - 


477,017,781 

fc 74,031 ,498 

1,7C8,753.2:8 

2,753,661,884 


87.501 
74568 
33,294 
83,797 


4,332,5S5 days, or about 12 " 
10,709.25:0 '"' " 29.1 " 
30,633.821 " " S4' •' 
60,126 720 " " 1341 " 





Rotation on their 
axis, in hours, min- 
utes, and seconds. 


Mass, 

(the Earth's Mass 

being unity.) 


Relative Density, 
(the Earth's Tensi- 
ty being unity.) 


Interior Planets. 


h. m. 6ec. 






Mercury, - 

Venus, - 

Earth, ... 

Mars, 


24 5 28 

23 21 8 

24 00 00 
24 39 21.67 


.1183 

.8S32 

1.0000 

.1324 


1.97 

0.92 
1.00 
0.72 


Exterior Planets. 








Asteroids, - 
Jupiter, - 

Saturn, ... 
Uranus, ... 
Neptune, - 


9 55 30 
10 16 4 


0.333 

338.0342 

101.0637 

14.7S89 

24.6483 


0.22 
0.11 
17 
0.31 



How many planets have moons, and what is the number of moons that each of 
these respectively have ? What is the known number of planets at the present time ? 
What the number of moons ? Are there reasons for believing that other planets will 
Le discovered ? Give the table of the planets ? 



KEPLER LAW OF DISTANCES. 199 

411. So vast are the numbers expressing the dis- 
tances of the planets from the sun, when a mile is 
taken as the unit of measurement, that the mind can 
scarcely grasp their meaning, and it is difficult to form 
a true conception of the immense spaces that separate 
these bodies from their central orb. A clearer idea 
may perhaps be conveyed by taking a different unit of 
measurement. 

412. From numerous experiments made by the 
American Coast Survey, it has been found, that the 
average velocity of electricity through the telegraphic 
wires is about 16,000 miles 'per second. At this rate 
a telegram can be sent across the continent, from 
New York to San Francisco, on a continuous wire, in 
about one-fifth of a second. Now supposing the sun 
was connected with the planets by telegraphic lines, 
then the t me it would take to transmit a message, 
From the Sun to the Earth, would be lh. 35m. 00s. 

to Jupiter, " 8h. 16m. 58s. 

to Saturn, u 15h. 10m. 56s. 

to Herschel, " Id. 6h. 31m. 59s. 
to Neptune, " Id. 23h. 48m. 20s. 

413. The apparent diameter of a body being in- 
versely proportioned to the distance (Art. 177,) at 
which it is viewed ; it follows, that the sun will appear 
of various sizes, at the different planets. The relative 

* Supjjosed new planet Vulcan. — On the 26th of March, 1859, Dr. Lescar- 
bauldt, of Orgeres, in France, beheld, moving across the sun's disk, a small, 
circular, and well denned dark object, which he regarded as a new planet 
in transit. Its apparent diameter was less than one-fourth of that of Mer- 
cury in transit. 

Leverrier, who considers the existence of one or more planets within the 
orbit of Mercury as highly probable, regards the observations of Dr. Les- 
carbauldt as worthy of credit ; and, upon the supposition that the planet 
moves in a circular orbit, estimates that its solar crrbit is 135,500,000 
miles, its periodic time 19d, 16h, and the inclination of the plane of its orbit 
12° 10'. J * J 

The supposed planet has been named Vulcan. 

How many planets have moons, and what is the number of moons that each of 
these respectively have ? What is the known number of planets at the present time ? 
What the number of moons ? Are there reasons for believing that other planets will 
be discovered ? Enumerate the planets and give their distances. What is said res- 
pecting our conception of these immense distances ? 

9* 



200 SOLAR SYSTEM. 

apparent magnitudes of this body as it would be seen 
from the principal planets are shown in Frontispiece. 

414. Kepler's law op Distances. From the third 
law of Kepler; viz., that the squares of the periodic 
times of the planets are as the cubes of their mean dis- 
tances from the sun, the unknown mean distance of a 
planet can be found, when its periodic time is ascer- 
tained together with the distance and periodic time of 
another planet. 

Thus the periodic time of Mars having been ascer- 
tained by observation, to be 687 days, and the distance 
of the earth from the sun and her periodic time being 
known, the mean distance of the former can be found 
by the following proportion; viz., the square of the 
earth's periodic time is to the square of Mars' periodic 
time, as the cube of the earth's distance is to the cube 
of Mars' distance. 

This proportion expressed in figures is as follows : 
365.256 representing the length of the year in days 
and fractions of a day, and 91,684,820 the mean solar 
distance of the earth in miles. (365.256 [days] x 
365.256) : (687 [days] x 687; : (91,684,820 [miles] 
X 91,684,820 x 91,684,820) : (139,700,000 [miles] x 
139,700,000 x 139,700,000.) The last term in the 
proportion is the cube of Mars' mean distance from 
the sun. The distance is therefore 139,700,000 
miles. 

415. In this way the periodic time of a planet can 
also be found when its distance is known, and also the 
distance and periodic time of another planet known. 
For reversing the terms of the proportion already 
given, the cube of the earth's solar distance is to the 
cube of Mars' solar distance as the square of the 
earth's periodic time is to the square of Mars' periodic 
time. 



Take the velocity of the electric current as the unit of measurement, and give the 
different estimates'of the planetary distances with this unit. What is said respecting 
the apparent size of the sun as viewed from the different planets? When can tne 
distance of a planet he found by Kepler's third law ? Give an instance. Can the 
periodic time of a planet he found by this rule? 



KEPLER LAW OF DISTANCES. 201 

416o The laws of Kepler are alike applicable to 
moons and planets; the mean distances of the former 
from the planets about which they revolve, can there- 
fore be determined, as in the case of planets, by the 
law just mentioned. Comets are also governed by 
the same laws. 

417. Bode's law of Distances. A relation between, 
the distances of the planets from the sun, was discov- 
ered in the latter part of the last century, by Prof. Bode 
of Berlin, it is termed Bode's law, and is thus expressed. 
If 4 is taken as the distance of Mercury from the sun, 4 
added to 3 gives the relative distance of Venus, 4 added 
to 3 x 2, that of the Earth, and the relative distances of 
the other planets are found in their order by succes- 
sively annexing 2 as a factor, thus, 

RELATIVE DISTANCES. 

Mercury, 4 =4 

Venus, 4 added to 3=7 

Earth, 4 " 3x2= 10 

Mars, 4 " 3x2x2=16 

Asteroids, (average distance,) 4 " 3x2x2x2= 28 

Jupiter, 4 " 3x2x2x2x2=52 

Saturn, 4 " 3x2x2x2x2x2 = 100 

Uranus, 4 " 3x2x2x2x2x2x2 = 196 

418. This law gives the actual distances of the above 
planets with tolerable exactness,when that of one of them 
is known. For example, the relative distance of Jupi- 
ter (52) : the relative distance of the Earth (10) : : the 
real distance of Jupiter, (477,017,781 miles) : the dis- 
tance of the earth (91,736,112 miles,) whichis nearly the 
true distance. Bode's law fails in the case of Neptune. 

419. Magnitudes. No relation has been discovered 
between the magnitudes of the planets by which the size 
of one can be ascertained, when that of another is known. 
These bodies differ very much in size, the asteroids being 
extremely small, while the bulk of others, as that of 
Jupiter and Saturn is immense, far exceeding the size of 
the earth. This subject with others of a kindred nature 

Is this law applicable to moons ? State Bode's law ? Is this law perfectly exact 1 Does 
it hold true ir. every case? When the magnitude of one heavenly body is known, ca» 
♦bat of another be inferred? Do the planets differ much in sizel 



102 



SOLAR SYSTEM. 



will be pursued farther in the subsequent pages, when 
each planet will be separately discussed. In Fig. 67, a 
view is presented of the relative magnitude of the eight 
chief planets. 

420. Division of the Planets with reference to 
the Earth. The planets with reference to the earth 
are divided into two classes. First, the Inferior 
whose orbits are within that of the earth : Mercury and 
Venus constitute this class. Secondly, the Superior 
whose orbits inclose the earth's orbit ; within this divis- 
ion are comprised all the planets from Mars to Neptune 
inclusive. 



INFERIOR PLANETS. 

421. The two planets Mercury and Venus are known 
to have their orbits within that of the earth ; First, be- 
cause they are never seen by us, like the other planets, 
in a part of the heavens opposite to that which the sun 
occupies, which would be the case if they included the 
earth within the circuit of their respective orbits. 

422. Secondly, if viewed with a telescope, they pre- 
sent phases like the moon ; being crescent shaped, when 
situated between the earth and the sun, and full when 
the sun is between them and the earth ; and in other po- 
sitions exhibiting every variety of phase between these 
two extremes. Phenomena which can be accounted for 
only on the supposition that these planets receive light 
from the sun, and move around it at a nearer distance 
than the earth. 

423. Thirdly, because these bodies at certain times are 
seen between the earth and sun, appearing as dark spots 
on his disk, as they cross from one side to the other. 
Such an appearance is termed a transit. 1 When either 
of these planets is between the earth and the sun, it is 
said to be in inferior conjunction, when the sun is between 
it and the earth it is in superior conjunction. 

1. Transit, see Art. 103, note 2. 

How are the planets divided in reference to the earth ? What is meant by an infe- 
rior, what by a superior planet T How do we know that the orbits of Mercury and 
V enus are within that of the earth ? What is the interposition of a planet between 
the earth and the disk of the sun called ? When are these planets respectively in 
their inferior and superior conjunction? 



DISTANCE OF MERCURY FROM THE SUN. 203 

MERCURY. £ 

424. This planet is the nearest to the sun of any that 
have been discovered. Its greatest angular distance 
from this luminary never reaches 29°. For this reason, 
it can only be discerned in the gloom of twilight, either 
at morning or evening, according as it is to the east 
or west of the sun. Even under the most favorable cir- 
cumstances, it does not appear conspicuous to the un- 
aided eye, but shines like a small star beaming with, a 
pale red light. 

425. Distance of Mercury from the Sun. The 
distance of this planet from the sun in miles, may be 
found, independently of the methods already explained in 
this chapter, by observing its angular distance from the 
sun at the time of its greatest elongation. 1 It is computed 
as follows. Let B, Fig. 68, represent the position of 

FIG. 68. 




Mercury at this period, S the sun, and E the earth ; draw 
the lines BS, SE, and EB, forming a triangle which will 
be right angled at B. The angle E, as taken by an in- 

1. Greatest elongation, by this is understood the greatest angular dis- 
tance that the planet departs from the sun, (as seen from the earth) while 
making a circuit around it. The greatest elongation in the case of Mer- 
cury occurs about 6 or 7 times a year. It never exceeds in extent as 
stati/d in the text 29° and is sometimes only about 16° or 17©. 

What is said respecting the proximity of Mercury to the sun ? What is the extent of 
Us greatest angular distance from this orb ? When can this planet be seen 1 When is it 
most conspicuous ? What is its appearance ? Expla'n how its distance from the sue ***, 
be caic ~..u:e<i < , 



204 SOLAR SYSTEM. 

strument, we will suppose is 22° 23', and we know the 
length of the line ES to be 91,684,820 of miles, be- 
cause it is the distance of the earth from the sun. 
Proceeding then, as we have often done before, we 
select a similar triangle S'E'B', and calling E'S 1 one 
mile, we make the following proportion ; E*S l (one 
mile) : S l B l (.370017thsof a mile) : : ES (91,684,820 
miles) : SB (34,913,671 miles.) 

426. If the orbit of Mercury was a perfect circle, one 
computation like this would give the true distance of 
the planet from the sun at any part of its orbit ; but 
Mercury revolves as the other planetary bodies in an 
elliptical orbit, and his distance from the sun is ac- 
cordingly variable. By making the preceding calcu- 
lation when the planet is in different points of its or- 
bit, the mean distance is ascertained, and found to be 
35,491,193 miles. 

427. Orbit — Inclination of its Plane. The ellip- 
tical orbit in which Mercury moves, deviates very 
much from a circle. At its perihelion the planet is 
about 28,250,000 miles from the sun's centre, while 
at the aphelion its distance is not far from 42,750,000 
miles. Its distance from the sun accordingly varies 
14,500,000 miles; a change nearly five limes greater 
than that which exists in the case of the earth, (Art. 
198.) The inclination of the plane of its orbit to that 
of the ecliptic is about 7°. 

428. Size — Apparent — Real. When Mercury is 
at his perigee, his apparent diameter is about 12'' but 
it decreases to 5" at his apogee. Knowing the dis- 
tance of Mercury from us, as well as his apparent 
diameter, it is easy to calculate his real diameter in 
the same way as we have computed that of the sun 
and moon, which has been repeatedly explained. From 
measurements taken with the utmost accuracy, the 
diameter of this planet is estimated to be 3,055 miles. 

Why will not one calculation give the true distance ? How is the mean distance 
obtained % What is it ? What is said respecting the orbit of Mercury ? How far is 
this planet from the sun at its perihelion and aphelion ? How great is the variation 
between the perihelion and aphelion distances' How does it compare with the vari- 
ation existing in the case of the earth ' What is the inclination of the plane of Mer- 
cury *s orbit to that of the ecliptic ' What is the apparent diameter of Mercury at 
its perigee and apogee t What is its actual diameter in miles ' 



ROTATION ON ITS AXIS. 205 

Very little difference is found to exist between its polar 
and equatorial diameters. 

429. Periodic Time. Mercury revolves about the 
sun in nearly 3 months, or more exactly 87d. 23h. 15m. 
Msec. The ancient astronomers by observing his re- 
turn to the same position in the heavens approximated 
very closely to his true period of revolution. By the 
application of Kepler's third law the 'periodic time is 
readily ascertained in the manner explained in Art. 414. 

430. Eotation on its Axis. The powerful illumi- 
nation to which this planet is subjected on account of 
its proximity to the sun, has thrown a degree of uncer- 
tainty upon all investigations respecting its physical 
characteristics. In consequence of this overpowering 
brilliancy it does not present in the field of the telescope 
a distinctly defined disk. The period also of observation 
is necessarily short, for in its rapid circuit, it soon ap- 
proaches the sun, and is shrouded from our view beneath 
the intense splendor of the solar rays. Moreover, since 
all observations must necessarily be made when the 
planet is near the horizon, it is consequently discerned 
through that part of the atmosphere which is most sub- 
ject to vapors, and is therefore liable to be seen distorted ' 
on account of the changeable nature of the medium 
through which it is observed. 

431. For these reasons the reliable observations upon 
Mercury are few. Sir William Herschel, with all his 
ability and skill, obtained no conclusive proof of the ex- 
istence of spots upon the surface of the planet which 
would have enabled him to determine the time of its ro- 
tation on its axis. Schroeter appears however to have 
met with better success. In the early part of this cen- 
tury he subjected Mercury to a most careful scrutiny 
and obtained, as he believed, decisive evidence of the ex- 
istence of mountains, rising to the lofty altitude of more 
than 10 miles above the general surface of the planet. 
By noting likewise the variation in the appearance of 

Is there any observed difference between the lengths of the polar and equatorial diameters ? 
What is theperiodic time of Mercury ? What is said respecting the observations of an- 
cient astronomers upon this planet ? Can the periodic time be obtained in any other way 
than by observation ? State why it is difficult to ascertain with certainty the physical 
characteristics of this planet? Are there many reliable observations on Merctirv ? State 
what is said respecting Sir William Herschel's efforts ? What success had Schroeter'' 



20(5 SOLAR SYSTEM 

the horns of the planet, when it assumed a crescent shape % 
the same astronomer ascertained to his own satisfaction 
the fact of its rotation ; the period of which he estimated 
at 24h. 5m. 28sec. Since the time of Schroeter no 
astronomer has gained any further information on 
these points, which future observations may modify or 
confirm. 

432. Phases. On examining Mercury with the tele- 
scope in different points of his orbit, we find that he 
presents phases like those of the moon in her revolution 
about the earth. 

433. When near his inferior conjunction,, or between 
the earth and sun, Mercury appears horned or crescent 
shaped, like the moon when new ; since nearly the whole 
of his illuminated hemisphere is now turned away from 
us in the direction of the sun. Advancing in his orbit 
to his greatest western elongation half of the illuminated 
hemisphere is then seen by us, and the planet is in its 
first quarter. As it moves towards its superior conjunc 
tion it becomes gibbous 1 the visible bright portion gradu- 
ally assuming a circular form, like the moon near the 
full. 

434. On account of the surpassing splendor of the 
solar rays, Mercury is invisible for some time before and 
after the superior conjunction, but on emerging into 
sight on the other side of the sun, he is still gibbous^ like 
the moon as she moves towards her third quarter. 

When the planet has arrived at its greatest eastern 
elongation, it again appears as a half moon, like our sat- 
ellite in her last quarter. As it approaches again its 
inferior conjunction, it dwindles once more to a crescent ; 
but is lost in the blaze of the solar light for some time 
before and after passing this position. 

435. Transit of Mercury. If the plane of the orbit 
of Mercury was coincident with that of the ecliptic, the 
planet at every inferior conjunction would pass directly 

1. See Art. 269, note 2. 

What is the period of Mercury's rotation as determined by him? Have later astrono- 
mers increased our knowledge of the physical characteristics of Mercury 1 What phe- 
nomenon is observed in respect to this planet, when viewed with a telescope? Descnba 
the phages of Mercury in full ? 



SPLENDOR OF MERCURY. 207 

between us and the disk of the sun, and wo ild appear as a 
black spot upon it. But since the plane of its orbit is in- 
clined to that of the ecliptic about 7° degrees, this phenom- 
enon does not occur at every inferior conjunction, for the 
planet may be on one side of the disk of the sun when it is 
in this position. 

436. In order that a transit may occur, the earth must 
be in the line of the nodes of Mercury, at or very near the 
time when the planet passes through one of them, in its 
revolution about the sun. For Mercury being at the 
node is consequently in the plane of the ecliptic, and the 
line of the nodes will then pass through the sun, the earth 
and Mercury, and the latter, as seen from the earth, will 
be projected as a dark spot upon the sun; just as the 
moon is during a solar eclipse. If the planet, the earth, and 
sun are not exactly in the line of the nodes, still a tran- 
sit may occur within certain limits, on account of the 
magnitude of the sun ; the planet crossing the disk of 
the sun not through its centre but on one side of it. 

437. The earth arrives at the line of the nodes twice 
a year, about the 10th of November and the 7th of May, 
and since the nodes move but about 13 / in one hundred 
years the transits of Mercury must for a long time hap- 
pen in these months. The last transit occurred on the 
8th of November 1848, l and the second after the next 
will happen on the 6th of May, 1878. 

438. Splendor of Mercury. The distance of the 
earth from the sun, is to the distance of Mercury from 
the sun in the ratio of about 8 to 3 ; and the nearer any 
planet is to the sun the greater is the amount of light it 

1. Respecting this transit, Prof. Alexander, of Princeton, thus speaks; 
" I observed that as the planet approached the sun it seemed to be united 
to it by a dark fringe or penumbra. During the progress of the transit 
Mercury was at times surrounded by a dusky ring. This occurred when 
the sun was slightly obscured by a thin haze. Occasionally also an ob- 
scurely luminous spot appeared upon the centre of the planet, this spot 
was united to the circumference by three fainter bands, symmetrically 
arranged " 

Why does not a transri of Mercury occur at every inferior conjunction ? What must 
be the respective positions of the planet and the earth that a transit may occur ? Why ? 
If these three bodies are not exactly in the line of Mercury's node can this phenomenon 
occur? Why? In what months do the transits happen? Why will they take place 
on these months for a long period ? When dii the last transit occur? When w*l] the 
"econd after the next take place 1 



20& SOLAR SYSTEM. 

receives. The intensity of the solar light at any two 
planets is inversely proportioned to the square of their dis- 
tances from the sun, accordingly the amount of light illu- 
mining a surface of one mile square on the planet Mercury 
is to that which falls upon the same extent of surface on 
the earth as 64 to 9. The intensity of light is therefore 
about seven times greater at Mercury than at the earth. 

439. The law of the decrease of the intensity of light 
with the increase of distance, is the same as that which 
exists in the case of gravity (Art. 394,) and may be il- 
lustrated by the same figure. Let therefore A., Fig. 69, 

FIG. 69. 




IHE INTENSITY OF THE SOLAR LIGHT VARIES INVERSELY AS THB SQUARE Of 
THE DISTANCE. 

be a point on the sun's surface from which light emanates, 
falling upon the squares BCDE, FGHI, JKLM. FGHI 
is twice as far from A as BCDE, and contains four times 
as much surface ; JKLM is four times as far from A as 
BCDE, and contains sixteen times as much surface. 
Now since the same quantity of light is diffused over each 
of the three squares, its intensity must be four times 
greater at the distance AB, than at the distance AF, and 
sixteen times greater than at the distance A J. 

440. The apparent surface of the sun, varies also ac- 
cording to the same law, and this luminary will conse- 
quently appear to the inhabitants of Mercury (if any 
there are) seven time <? larger than it does to us. 

441. Mass and Density. The investigations of as- 
tronomers in respect to these particulars have led to the 

What is said respecting the amount of solar light received by a planet ? What in th« 
law of its intensity? Explain why the intensity of solar light is seven times greater al 
Mercury than at the earth 1 Illustrate the above law from the Figure. How does the ap 
parent surfuce of the sun vary 1 How much larger would it appear at Mercury than i» 
does a\ the earth '! 



VENUS APPARENT DIAMETER. 209 

conclusions, that the mass of the earth is about eight 
times greater than that of Mercury, and the density of 
the planet twice as great as that of the earth. 

442. Ancient observations of Mercury. The 
earliest recorded observation of this planet was made 
60 years after the death of Alexander the Great, on the 
15th of November, 265 years before Christ. On the 
19th of June, 118 A.D., the Chinese astronomers like- 
wise observed Mercury to be near the Beehive, a cluster 
of stars in the constellation of Cancer, retrograde calcula- 
tions by modern astronomers have shown, that on the 
evening of this day Mercury was distant from this 
group of stars less than one degree. 

VENUS 9 

443. Distance and periodic time. We now come 
to Venus the second planet in order from the sun, and 
the most beautiful star that adorns the heavens. Her 
mean distance from the sun is 68,770,000 miles, and she 
revolves about this luminary in 224£ days, or more ac- 
curately 224 days 16h. 49m. 8sec. 

444. Apparent diameter. The apparent diameter 
of Venus varies much more than that of Mercury, ow- 
ing to the fact that the changes in the distance of this 
planet from the earth, are much greater. When Mer- 
cury is nearest to us, he is in round numbers but 
48,000,000 miles distant, and when most remote, recedes 
from us only 135,000,000 miles; but Venus at times 
comes as near to the earth as 24,000,000 miles, and then 
withdraws from it to the distance of about 159,000,000 
miles. This great change in the distance is shown, as 
in the case of the moon, by the variation in the planet's 
apparent diameter, for when it is at its inferior conjunction 
its diameter measures 66'', while at its superior, it is 
more than six times smaller, being about 10". 

445. Real Diameter. This is not very precisely 

State what is said respecting the mass and density of Mercury ? What are the 
earliest recorded observations of this planet ? What is said respecting Venus ? What 
is her distance from the sun ? What her periodic time ? Why does the apparent di- 
ameter of Venus vary more than that of Mercury ? What is the greatest apparent 
diameter of Venus ? What the least ? 



210 SOLAR SYSTEM. 

known, but according to the best observations, its length 
is about 7,700 miles, which is very nearly the same as 
that of the earth. No astronomer as yet has been able 
to determine by observation the exact difference be- 
tween the polar and equatorial diameters of Yenus. 
That a difference exists is evident from the rotation 
of the planet on its axis, but the amount of difference 
is unquestionably small. 

446. Rotation. The intense splendor of Yenus in- 
vests every part of her disk with such a brilliant light 
that any variation in the surface of the orb for the most 
part escapes detection, since the valleys as well as the 
mountains, if such inequalities exist, are bathed in 
floods of light ; and astronomers therefore speak doubt- 
ingly of cloudy spots upon the surface of the planet. 

447. It is usually by directing their observations to 
well defined spots, that astronomers determine the period 
of the rotation of a planet upon its axis ; the absence of 
such marks upon Yenus, for a long time, rendered the 
time of her rotation a matter of uncertainty. One as- 
tronomer, Cassini, in 1667, fixed it at 23h. 16m. and an- 
other, Bianchini, in 1726, estimated it to be 24 days and 
8 hours. At last Schroeter, the celebrated German astron- 
omer, by directing his attention to a mountain, which he 
discovered near the southern horn of the planet, ascer- 
tained from eight observations, that this orb revolves on 
its axis in 23h. 21m. and 8sec. This result has been 
almost universally received, though it is not regarded 
by astronomers as exact beyond the possibility of an 
error. 

448. According to the observations and calculations 
of the same astronomer, mountains exist on the surface 
of Yenus, of the surprising height of fifteen or twenty 
miles, but no great confidence has been placed on these 
determinations, since the diameters of some of the small 
planets, as ascertained by Schroeter, are found to be 

What is the extent of the real diameter of Venus ? Has any difference been observed 
Between the polar and equatorial diameters 1 Must there be a difference? Why do we 
know scarcely anything respecting the surface of this planet 1 What is said in regard t» 
the existence of spots ? How do astronomers ascertain the fact and time of a planet's r<» 
tation ? State by whom, and in what manner the rotation of Venus was discovered, and 
the period of the same determined? Is this period of Venus' rotation considered by tu- 
tronnmers as absolutely exact? What is said of the mountains of Venus? 



PHASES. 211 

much greater than those obtained by later astronomers 
with their improved and finely constructed instruments. 
It is therefore not improbable, that the want of accuracy 
and delicate refinements .n his instruments led to the 
very great altitudes which Schroeter assigned to the 
mountains of Yenus. 

449. Orbit — Inclination of its plane to that of 
the Ecliptic. Unlike that of Mercury the orbit of 
Venus is almost a circle. We have seen that the mean 
solar distance of Venus, is 66,318,381 of miles; if her 
orbit was a circle she would always be at the same dis- 
tance from the sun, but the latter is a littfe out of the 
centre of the planet's orbit; so that when Venus is at 
her aphelion she is about 970,000 miles farther from the 
sun than when at her perihelion. This variation is 
much less than it is in the case of Mercury ; whose solar 
distances at these points differ to the extent of 15,000,000 
miles, (Art. 427.) The inclination of the plane of the 
orbit of Venus to that of the ecliptic is about 3° 23' 
(more nearly 3° 23' 29".) 

450. Phases. In her revolution about the sun Venus, 
like Mercury, presents to our view similar phases to 
those of the moon. But since this planet is nearly twice 
as far from the sun as Mercury, and its real diameter is 
almost three times greater, these phenomena are more 
conspicuous, and can be observed for longer consecu- 
tive periods. 

451. In a certain part of her orbit we behold this 
beautiful planet rising a little before the sun, when it is 
termed the morning star. It has then just passed its 
inferior conjunction and its dark side is turned towards the 
earth, like that of the moon when she is new. Venus now 
moves rapidly westward from the sun, rising every day 
earlier and earlier before this luminary, until she attains 
her greatest western elongation which is about 47° 15'. 
At this point of her orbit she rises between three and four 
hours before the sun, distinguished for her peerless splen- 

What is remarked respecting Schroeter's observations on the mountains of Venus ? State 
what is said in regard to the orbit of Venus ? What is the difference between Venus' pe- 
rihelion and aphelion distances? How does this difference compare with Mercury's? 
What is the inclination of the plane of the orbit of Venus to that of the ecliptic? Why 
are the nhases of Venus more conspicuous than those of Mercury ? 



212 SOLAR SYSTEM. 

dor among the stars that sparkle in the eastern sk) 
She is now in her first quarter, only one-half of her en- 
lightened hemisphere being visible through the tele- 
scope, to the inhabitants of our globe. 

452. Still moving onward in her orbit Venus departs 
from her greatest western elongation towards her supe- 
rior conjunction, and in so doing approaches the sun. 
She now rises later and later every day, her illumined 
disk becoming gibbous, like that of the moon in her 
■second quarter, as is readily seen by the aid of the tele- 
scope. At length she arrives at her superior conjunction, 
when she is seen as the moon at the full, her bright disk 
being nearly circular. 

453. A period of about nine months elapses from the 
time that Venus is first seen in the morning until she thus 
reaches her superior conjunction. Passing this place in 
her orbit the planet now appears on the other side of 
the sun (the eastern side,) rising after this luminary, and 
is consequently invisible to the naked eye, from the in- 
tense splendor of the solar light. But rising after the 
sun, the planet must necessarily set after it, and since 
the time of its setting grows later and later as it advan- 
ces in its orbit, we at length see it beaming in the 
western sky soon after the solar orb has sunk beneath 
the horizon. 

454. The planet is now the evening star, and by telescopic 
aid we perceive that its visible form is no longer circular 
but appears gibbous like the moon approaching her third 
quarter. Gradually Venus departs more and more from 
the sun, until she attains her greatest eastern elongation, 
at which point she is again seen through the tele- 
scope in the shape of a half moon. After reaching this 
limit, the planet returns towards the sun, resuming its 
crescent form. Having passed the sun it recommences 
its course as the morning star, going continually through 
the above series of changes. Fig. 70, is a representation 
of Venus as she appears when viewed through a tele- 
scope near her inferior conjunction. 
455. Splendor of Venus. Venus shines with the 

Describe the phtises in full ? 



SPLENDOK OF VENUS. 213 

FIG. 70. 




TELESCOPIC APPEARANCE OF VENUS WHEN NEAR HER INFERIOR 
CONJUNCTION. 

greatest brilliancy when her angular distance from the 
sun is a little less than 40°. l About once in eight years, 
under a favorable concurrence of circumstances, her 
splendor is unusually great. The brightness of the 
planet is then so intense that under a serene sky it can 
be seen even at noon day. 

456. On account of the proximity of Venus to the 
sun, the intensity of the solar light is about twice as great 
on this planet as it is at the earth. For since their re- 
spective distances from the sun, are nearly as 2 2 to 3, the 
degree of illumination which each receives will be ex 
pressed, according to the law of diffusion already stated 
(Art. 439,) by the numbers 4 and 9, which are nearly in 
the ratio of 1 to 2. 



1. Venus does not appear brightest when she is nearest to the earth, 
because only a small portion of her illumined surface is then turned towards 
us. Neither is she most splendid when nearly all her illuminated hemis- 
phere is presented to our view, because she is then farthest from us, and 
her apparent diameter is as small as possible. Her place of greatest bril- 
liancy is therefore between these two positions, and is found, as stated in the 
text, to be a little less than 40° from the sun. 

2. The earth's solar distance is about 95,000,000 miles. . That of Venuo 
nearly 68,000,000. The latter distance is therefore to the former in the 
ratio of about 2 to 3. 

State what is said of the splendor of Venus ? How much greater is the intensity of the 
•olar light at Venui than at the earth ? Whv 1 



214 SOLAR SYSTEM. 

457. Mass — Density. The mass is ascertained by va- 
rious methods, and from the latest and most accurate in- 
vestigations it appears, that the sun contains 360,000 
times more matter than Venus. She has therefore a little 
less matter than the earth, since the mass of the sun is 
only 317,000 times greater than that of the earth. The 
density of Venus nearly equals the density of the earth, 
the former being to the latter, as 92 to 100. 

458. Atmosphere of Venus. Various observations 
have been made by astronomers upon this planet, which 
have led them to suspect that it is enveloped in an at- 
mosphere. Beyond the true extremity of the horns 
when Venus appears crescent-shaped a fine streak of pale 
blue light has been not un frequently seen, projecting 
over the unilluminaied part of the orb, and which has 
been regarded as a twilight, i. e. light reflected from an 
atmosphere. Sir William Herschel noticed a luminous 
border around the planet, from which phenomenon 
he inferred that Venus possessed a dense atmosphere. 
The bright border being caused by the reflection of light 
from the particles of air composing the latter. Moreover, 
during a transit of Venus, various appearances occur 
which lead to the belief that an atmosphere surrounds 
this orb almost as dense as the atmosphere of the earth. 

459. Transit of Venus. This appellation is given, 
as in the case of Mercury to the passage of Venus across 
the sun's disk. A high importance is attached to this 
phenomenon by astronomers, since by means of it they 
are enabled to obtain with great accuracy the parallax 
of the sun, without which the distance of the earth from 
the sun could not be determined. 1 The manner in 
which the parallax is obtained, it is not difficult to un- 
derstand, but the various mathematical processes which 

1. In order to ascertain the solar distances and the magnitudes of the 
planets, we have seen that the distance of the earth from the sun must be 
first known. It is also needed in order to determine the solar distances of 
some of the fixed stars, as will be shown in Part III. The accurate deter- 
mination of the sun's parallax, is therefore of the utmost importance in as- 
tronomical researches. 

What is the mass of Venus ? What her density 1 What nppearances have led astrono- 
mers to suspect that this planet is possessed of an atmosphere 7 What is said in regard to 
the transits of Venus ? 



TRANSIT OF VENUS. 215 

conduct to the result are too complicated and abstruse to 
be admitted into an elementary work like this. 

460. Let E, V, and S, Fig. 71, represent the relative 
positions of the earth, Venus, and the sun when a tran- 

FIG. 71. 




sit takes place, HVI a portion of the orbit of Yenus, 
and FG, a diameter of the earth perpendicular to the 
ecliptic. If at the time of the transit two spectators 
were respectively placed at F and G-, the diameter of 
Dhe earth apart, the observer at F would see Yenus 
in the direction FY, projected as a dark spot on the sun 
at/ and, at the same instant, the person at G would in 
like manner behold the planet in the direction GV, pro- 
jected on the sun at e. 

"461. That such would be the case is evident from va- 
rious familiar examples. Thus for instance if a tree is 
standing in the middle of a square field, and one person 
views it from the south-east corner of the lot, while a 
second beholds it from the north-east corner ; the first 
sees the tree against the north-west portion of the sky, 
while the second observes it in the south-west quarter of 
the heavens. 

462 . Yenus in the above position is on an average 66,- 
000,000 miles from the sun, and 26,000,000 miles from 
the earth, for the distance of Yenus from the earth is 
nearly equal to 92,000,000 miles, diminished by 66,000,- 
000 miles, i.e. 26,000,000 miles. If we suppose e and/ 
to be joined by a straight line, two similar triangles are 
formed; viz., FYG and eV/ whose sides are propor- 
tional. Considering FG as equal to 1 we then institute 

Explain by the aid of Figure 71. in what manner the sun s horizontal parallax is ol* 
tained bv observations on the transit of Venus? 

10 



216 SOLAR SYSTEM. 

the following proportion ; to wit, GY (26,000,000 miles) ; 
Ve (66,000,000 miles) : : FG (1) : ef. By the rule of 
three efis found to be nearly equal to 2i, that is, it is two 
and a half times greater than FG-. 1 

463. If therefore the line FG (the earth's diameter) were 
placed upon the sun, it would occupy about fths of the 
extent of ef, and the angular measurements of these two 
lines, as viewed from the earth would be nearly in the 
same ratio. But the Sufi's horizontal parallax (Art. 94,) 
is the angle under which the earth's radius is seen at the dis- 
tance of the sun from the earth, it must therefore be equal 
to }th of the angle which the line ef measures at the dis- 
tance of the earth from the sun. 2 The value of this an- 
gle can be ascertained when each observer notes at his sta- 
tion the exact time occupied by the planet in crossing the 
dish of the sun, and one-fifth of this value is the sun's 
horizontal parallax. 

464. The last transit of Yenus, from the observations 
upon which the value of the sun's horizontal parallax as 
now received was obtained, took place in 1769. Exten- 
sive preparations were made in various quarters of the 
world for ensuring the most available and accurate obser- 
vations. Capt. Cooke was sent by the British govern- 
ment to Tahiti, and many other European powers dis- 
patched their ablest astronomers to places most eligible 
for this purpose. The farther apart the observers are, 
the greater will be the displacement of Yenus on the 
solar disk, and the greater the difference in the duration 
of the respective transits ; but this difference is small at 
the best, and therefore astronomical stations are sought, 
which are widely separated from each other. On this 
account the observations which were taken at Tahiti, in 
the South Seas, and at Cape Wardlaus in Lapland, wero 
of great importance. 

1. The solar distances of Venu3 and the Earth are here employed for the sake of 
convenience. The ratio hetween GVand Ve can be found without them, by ob- 
servations upon Venus at her greatest elongations. 

2. The radius of the earth which is the AaZ/of FG, must evidently 
equal ^th of ef. 

When did the lust transit of Venus occur 1 What preparations were then made by th« 
various governments of Europe ? What observations were of great use ? Whv ■? 



EARTH SUPERIOR PLANETS. 217 

465. The result obtained gave for the sun's parallax 
8' .5776. But doubts have existed as to the genuineness 
ot the observations at Wardlaus, and recent investiga- 
tions show that this value is too small. 

466. Value of the Solar Parallax. The solar par- 
allax is derived from three other independent methods, 
viz: By observations on Mars in opposition; by the 
sun's disturbance of the moon's motion ; and by the 
velocity ot light. The parallax obtained by the first 
method varies from 8". 5 to 10". 20 ; by the second from 
7".8 to 8'\95; and by the third from 8".51 to 8". 86. 
From the investigations which have been made, it is in- 
ferred that the best approximate value of this parallax 
is 8". 9. The next transit of Venus takes place Pec. 
8, 1874, and another Dec. 6, 1882, and to these astono- 
mers look for its precise determination. 

THE EARTH. © 

467. The next planet is the Earth. This with its at- 
tendant moon we have already discussed and therefore 
pass on to the superior planets. 

SUPERIOR PLANETS. 

468. These celestial bodies are more distant from the 
sun than the earth is, and their orbits consequently encir- 
cle that of the earth. They are in superior conjunction 
when the sun is directly between them and earth, and in op- 
position when the earth is directly between them and the 
sun. As they can never come between the earth and the 
sun, it is of course impossible that they should have any 
inferior conjunction ; on this account they are not subject 
to phases like those of Mercury and Venus. Moreover 
they are seen at all angular distances from the sun, from 
0° to 180°. In these three respects, as viewed from the 
earth, they differ from the inferior planets. The next 
planet in order is Mars. 

"What is the value of the sun's horizontal parallax as deduced from these observa- 
tions ' Is this perfectly exact? Why not? By what other methods is the solar par- 
allax computed ? What results have been obtained by them ? What is the most re- 
liable value of the solar parallax ? When do the two next transits of Venus occur, 
and what is expected to be ascertained by means of them ? What is the next planet 
in order ? What is said of it ? What is said respecting the superior planets ? Have 
they any inferior conjunction 7 State the three particulars in which they differ from 
the inferior planets as viewed from the earth ' to hat superior planet is next in order ? 



218 SOLAR SYSTEM. 

MAES. 6 

469. Distance — Orbit — Inclination of the plane 
of the orbit. This planet is situated at the average 
distance of about 139,700,160 miles from the sun, but 
as the orbit in which it moves is an ellipse that deviates 
very much from a circle, the difference between its peri- 
helion and aphelion distances is very considerable. The 
former amounting to about 152,700,000 miles, and the 
latter to 127,300,000 miles, their difference being 25,- 
400,000 miles. The inclination of the plane of the or- 
bit of Mars to that of the ecliptic is about 1° 53'. 

470. Periodic Time. The period of time occupied 
by Mars in making one revolution about the sun, is ac- 
cording to the best computation, 686 days 23h. 30m. 
41sec. 

471. Real and Apparent Diameter. The real 
diameter of Mars is about 4,500 miles, but his apparent 
diameter is subject to great variations ; for at the time of 
his superior conjunction when he is most remote from us, 
his apparent diameter measures only a little more than 
4'' , but when nearest to us, and in opposition, it is 
about 24". 

472. On this account, Mars when nearest to us shines 
with great splendor, and rising about sunset moves along 
the sky a conspicuous object throughout the night, but 
when most remote from the earth he appears like a star 
of ordinary size. The cause of these great changes is 
readily perceived, when we consider, that in as much as 
the orbit of Mars includes that of the earth, his distance 
from the earth at superior conjunction, equals his own 
distance from the sun increased by that of the earth's 
solar distance, and at opposition it is only equal to the 
difference of these distances. Stating the same in figures, 
the distance of Mars from the earth at superior conjunc 
tion, amounts in round numbers to 140,000,000 miles, 
added to 95,000,000 miles, or 232,000,000 miles, while at 
opposition it is equal to 142,000,000 miles diminished bv 

What is the solar distance of Mars? What is said of its orbit? What is the inclirm- 
tion of its plane to that of the ecliptic ? What is his periodic time ? What is the length 
of the real diameter of Mars ? What is said respecting the chunges in his apparent dr 
imeter? When is it greatest? When least? What is said of the changes in the 
splendor of Mars ? Explain the cause of these variations 1 



PHASES OF MARS. 219 

92,000,000 miles or 48.000.-000 miles. A variation in 
distance so extensive as this, must of course give rise to 
corresponding changes in the apparent size and brilliancy 
of the planet. 

473. Phases. Although Mars never exhibits phases 
like those of Mercury and Yenus, his illuminated sur- 
face is nevertheless subject to slight fluctuations in form. 
At the time of opposition the planet is exactly circular 
but in other positions is oval, owing to the cir- 
cumstance that we then view it out of the line joining the 
centre of the planet and the sun, and therefore lose sight 
of a part of the surface that is illumined by the solar 
rays. 

474. This point is illustrated by Fig. 72, where S rep- 
resents the sun, the circle around it the orbit of the 

FIG. 72. 




PHASES OF MARS. 



earth, E and E 1 two positions of the earth, and M, Mars. 
Now since half of the surface of Mars is illumined by the 
sun, the boundary of the visible portion, as seen from 
the sun, may be represented by the line ab drawn perpen- 
dicular to the line joining the centres of the sun and 
Mars. To a spectator at S the shape of Mars would be 

Does this planet exhibit phases like those of the inferior planets ? To what change* if 
iU visible surface subject 1 Explain the cause 7 Illustrate from Figaro. 



220 SOLAR SYSTEM. 

a circle, and it would be the same to a person on the 
earth, when the earth is at E 1 , Mars being in opposition 

475. But when the earth is at E, a part of the enlight- 
ened hemisphere of Mars is invisible to a spectator at E ; 
for that which is included between the lines ab and cd 
has passed out of view and he can see no farther than c 
in the direction of a. Accordingly when the sun, 
the earth, and Mars are situated as in the figure, the 
planet as seen from the earth will appear of an oval shape. 

476. The form of the visible surface of Mars becomes 
more and m,ore oval from opposition to quadrature 1 ; in 
which position the planet resembles the moon a day or 
two before her third quarter, and accordingly is generally 
seen gibbous ; but even then, the illuminated surface is 
never less than seven-eighths of a circle. 

477. Physical Aspect — Atmosphere. When 
viewed through a telescope of adequate power, the out- 
lines of continents and seas are revealed on the surface 
of Mars, while near the poles, at the planet's latitude of 75° 
or 80°, ivhite spots are discerned, which, from their in- 
crease and decrease with the change of its seasons, have 
been regarded by Sir Wm. Herschel as masses of ice and 
snow that accumulate during the winter of Mars, and 
diminish in the summer. The continents appear of a 
dull red hue while the seas possess a greenish Hinge. The 
ruddy hue of the planet, is attributed by Sir John Her- 
schel to the prevailing color of the land. 

478. It was formerly supposed that the red hue of 
Mars was owing to a very dense atmosphere, but late 
observations of astronomers show that the atmosphere 
is of medium density. Recent spectroscopic observa- 
tions corroborate the view of Herschel, and also indi- 
cate the presence of water in the atmosphere of Mars. 

1. For the meaning of quadrature^ see Art. 272. 

2. The greenish tinge is supposed by Herschel to be the effect of con- 
trast. For example if we gaze steadily upon a red wafer for a considera- 
ole time and then look upon a white object as a piece of paper, the latter 
will appear of a blueish green hue. 

What variations take place from opposition and quadrature 1 What is the phase of 
Mars at quadrature 1 What portion of a circle does the illuminated surface measure 
when least ? Describe the physical aspects of Mars ? What is said respecting the exis- 
tence of an atmosphere ? 



DENSITY — MASS. 221 

479. Rotation. The rotation of this planet on its 
axis has been determined by observing the spots upon 
its surface. The time of rotation was estimated by 
SirWm. Herschel, at 24h. 39m. 21.67sec, but Prof. 
Madler from recent observations reduced this time to 
24h. 37m. 20sec. which may be regarded as the length 
of a day on the planet Mars. 

480. Inclination of the axis. Observations upon 
the spots have shown that the axis about which Mars 
rotates is inclined to the plane of his orbit at an angle 
of 61° 18'. This quantity is very neaaly equal to the 
inclination of the earth's axis to the plane of its orbit, and 
as the seasons depend in a measure upon this inclination, 
those of Mars are probably somewhat like our own. 

481. Ellipticity. The rotation of Mars necessarily 
produces a difference in the length of the polar and equa- 
torial diameters, the planet being flattened at the poles and 
swelled out at the equator. This compression was, until 
lately considered to be very great, the ratio of the polar 
to the equatorial diameter being according to Sir Willam 
Herschel, as 15 to 16 ; so that if the length of the equa- 
torial diameter of this planet is reckoned at 4,354 miles, 
that of its polar diameter is only 4,082 miles ; the latter 
being thus 272 miles shorter than the former. 

482. But according to Mr. J. R. Hind, an extensive 
series of very accurate observations, recently taken with 
the best instruments, make the compression much less, 
the ratio of the diameters being as 51 to 50, which result 
is regarded as being much nearer the truth than tho 
estimate of Herschel. According to this computation 
the difference between the polar and equatorial diame- 
ters of Mars, is only about 85 miles. 

483. Density — Mass. The density of Mars is nearly 
three-fourths of that of the earth, the former being to 
the latter as 72 to 100. The quantity of matter con- 
tained in this planet is about eight times less than that 
contained in our globe. 

How has the rotation of Mars been determined 1 What is its period ? What is the in- 
clination of the axis of rotation to the plane of the orbit of Mars 1 What is observed in 
regard to the seasons of this planet 1 What is said respecting the ellipticity of Man 1 
What is its extent according to Sir William Herschel ? What according to Mr. J. B 
Hind 1 What is *he density of Mars ? The mass ? 



222 SOLAR SYSTEM. 

484. Intensity of solar light. The relative intensi 
ties of the solar light at Mars and at the earth, as found 
by the rule already given (Art. 439,) arerepiesented by 
the numbers 43 and 100. To illustrate, if on a given 
surface the earth receives 100 solar rays, Mars receives 
on the same extent of surface only 43 rays. 

485. Fig. 73, represents Mars as viewed by the ac- 
complished astronomer Sir John Herschel, in his 20 feet 

FIG 73. 



MARS AS SEEN BY SIR JOHN HERSCHEL. 

telescope, on the 16th of August, 1830. It show? Uw 
planet in its gibbous state, with the outlines of its cu/di? 
ncnts and seas ; while one of the white spots which are 
sitiated near its poles is distinctly discernable on its 
surface. 

THE ASTEROIDS, OR PLAXET0IDS. 

486. The astronomer Kepler, 270 years ago, noticed a 
tendency to a regular progression in the distances of the 
planets from the sun, as far as Mars. Twice the distance 
of Mercury from the sun, is nearly the distance of Venus, 
three times that of Mercury is about the distance of the 

What the re.'ative intensities of the solar light at the earth and at Mars ? Whnt does 
Fig. 73, represent ? What did Kepler remark in regurd to the solar distances of the planets 1 



THE ASTEROIDS. . 223 

earthy and four times the distance of Mercury gives almost 
exactly the distance of Mars. But in order to represent 
the distance of Jupiter, between which orb and Mars no 
planet in the time of Kepler was known to exist, the 
distance of Mercury must be multiplied not by 5 but 
by IS. 

487. The law appeared here to be broken, and an im- 
mense interval of 350,000,000 miles, extending between 
Mars and Jupiter, to be unoccupied by a single planetary 
body. Kepler imagined that in order to preserve the 
harmony of distance another planet existed in this vast 
space, which had hitherto eluded the searching gaze of 
astronomers. 

488. For two centuries nothing was done to verify or 
overthrow this hypothesis of Kepler ; but when in 1781 
Uranus was discovered by Sir Wm. Herschel, an im- 
pulse was given to astronomical investigations, and an 
association of astronomers commenced a systematic 
search for this supposed planet, whose probable distance 
they determined by the law of Bode. Ere long instead 
of one, four small planets were discovered to which were 
assigned the names of Ceres, Pallas, Juno, and Yesta. 

489. Nearly 50 years more elapsed when the search 
was renewed in the same region of space, and the dis- 
covery of one hundred and five additional asteroids has 
rewarded the labors of the astronomer. 

490. Two circumstances enable an observer to dis- 
tinguish a planet from a fixed star. First, the latter 
class of heavenly bodies as ordinarily viewed, always 
keep at the same distance from each other. Secondly, 
how much soever a fixed star is magnified, it still ap- 
pears as a mere point of light on account of its immense 
distance from us, while a planet has a round dish like the 
moon. When therefore an astronomer, watching a star 
from night to night, beholds it gradually approaching the 
assemblage of fixed stars, that are situated on one side 
of it, and receding from those on the other, he pronoun- 

Where was this law broken 1 What did this fact lead him to think ? Was anything 
done by the astronomers, who immediately succeeded Kepler to confirm or overthrow 
his hypothesis 1 When was a new impulse given to astronomical research, and why T 
What was then done by astronomers ? What success has attended this search for planets 1 
How can a planet be distinguished from & fixed star ? 
10* 



224 SOLAK SYSTEM. 

ces it at once a planet ; and if he is also able to discern a 
round well-defined dish he possesses an additional proof of 
the planetary nature of the body. 

491. The discovery of planets has been very much 
facilitated by the use of celestial maps and charts, where 
the stars are now laid down with such precision, that if 
one, which has been regarded as fixed, is really a planet, 
its departure from the place assigned it on the map is 
very soon detected, and its true character known. 

492. We shall now proceed to speak briefly of the 
first five asteroids, taking them in the order of their 
discovery. 

CERES. 9 

493. On the 1st of January, 1801, Prof. Piazzi, of 
Palermo, while searching for a star which was mapped 
down on a star-chart, but which he could not find in the 
heavens, observed an object near the place of the missing 
orb, shining like a star of the eighth magnitude 1 and 
which he took at first to be a comet, but which proved 
to be a planet It was soon afterwards lost sight of on 
account of its nearness to the sun, but on the 1st of 
January, 1802, it was re-discovered by Dr. Olbers, of 
Bremen. In March, 1802, a friend of Prof. Bode, beheld 
the planet with the naked eye, though it generally re- 
quires the aid of a telescope in order to be discerned, as 
it is just beyond the limit of unassisted vision. 

494. The smallness of Ceres has precluded any very 
exact measurements of her size. According to Sir Wm. 
Herschel's observations she is only 163 miles in diame- 

1. Eighth magnitude. The stars are divided into classes according to 
their apparent brightness. The brightest are termed stars of the first 
magnitude. Those which are nearly as brilliant, but whose splendor is yet 
perceptibly less, belong to the second magnitude. This classification is 
extended down to the sixteenth magnitude. The sixth or seventh magni- 
tudes includes the smallest stars visible to the naked eye under the most 
favorable circumstances. All the stars below these magnitudes require a 
telescope to render them discernible. In Part III. this subject will be 
more fully discussed. 

What has facilitated the discovery of planets? Of what hodies are we now to speak! 
By whom was Ceres discovered ? When and under what circumstances t How larg« 
does she appear 1 



PALLAS — JUNO. 225 

ter, while other astronomers estimate her diameter at 
about two hundred and twenty miles. Her mean distance 
from the sun is 253,600,000 miles, she revolves around 
it in about 1,681 days, and inclination of the plane 
of her orbit to that of the ecliptic is little more than 
10° 37'. This planet shines with a pale reddish light, 
and a slight haziness that envelopes it has led some to 
think, that it is possessed of an atmosphere. The sym- 
bol of Ceres, the goddess of agriculture, is the sickle. 

PALLAS. $ 

495. While Dr. Olbers on the 28th of March, 1802, 
was examining various groups of stars, which lay near 
the path of the planet Ceres, he found a star in a posi- 
tion where he was certain none was visible during the 
two preceding months. The observations of the same 
and the succeeding evening showed that it evidently 
moved among the fixed stars — a new planet was found, to 
which the name of Pallas was given, and the lance head 
indicative of the character of the goddess was selected 
as its symbol. 

496. Pallas shines as a star of the seventh magnitude 
with a fine yellowish light. A haziness, less dense than 
that which belongs to Ceres, has been noticed by some 
astronomers encircling the planet, and has led them to 
conjecture that Pallas is also surrounded by an at- 
mosphere. 

497. The diameter of this planet, as determined by 
Dr. Lamont of Munich, is 670 miles, but other observ- 
ers estimate its diameter at about 170 miles. Its mean 
distance from the sun is 253,966,951 miles, its periodic 
time 1,684 days, and the inclination of the plane of its 
orbit to that of the ecliptic 34° 37' 20". 

JUNO. 5 

498. This asteroid was discovered by Prof. Hardmg, 

What is her diameter? Mean solar distance and periodic time 1 What is the inclina- 
tion of the plane of her orbit to that of the ecliptic 1 What is her color 1 Has she an at- 
mosphere 7 What is her symbol? Who discovered Pallas, and in what manner? At 
what time 1 What is her symbol 1 How large does Pallas appear ? Has she an atmos 
phere 1 What is her diameter ? Mean solar distance and periodic timt "i What i« »*•« 
inclination of the plane of her orbit 1 



226 SOLAR SYSTEM. 

of Lilienthal, on the 1st of September, 1804, while form- 
ing charts of small stars lying in the paths of Ceres and 
Pallas. At ten o'clock on the evening of this day he 
observed a star near several others in the constellation 
of the Fishes, which on the evening of the 4th had 
changed its place, and continued to do so night after 
night. The name of Juno was given to this planet, and 
as Juno was queen of Olympus, a sceptre crowned by a 
star was chosen as the symbol of the asteroid. 

499. This planet appears as a reddish star of the eighth 
magnitude. Its mean distance from the sun is 244,- 
800,000 miles, its period of revolution 1,592 days, and 
the inclination of the plane of its orbit to that of the 
ecliptic is 13° 3' 17". 

VESTA, fi 

500. After the discovery of Pallas, Dr. Olbers noticed 
that the orbits of Pallas and Ceres approached very near 
each other at one of the nodes of Pallas, a circumstance 
which led him to think that these two bodies were but 
fragments of a larger planet, which once existed between 
Mars and Jupiter, at the mean solar distance of Ceres 
and Pallas, and was shivered to pieces by some tremen- 
dous convulsion. Other fragments yet undiscovered he 
believed were still moving in space, and although the 
planes of their orbits might be differently inclined to that 
of the ecliptic, yet as they all had the same origin he 
supposed there must be two points in the orbit of each 
through which the rest at some time or other must ne- 
cessarily pass. These two points are the places where 
the planes of the orbits of these fragments intersect one 
another. 

501. By watching these points he thought it not im 
possible that some of the flying fragments might be de- 
tected ; it was in one of these that Juno was found, and 
other planets might reward a systematic search. The 

Bywhotti was Juno discovered 1 When 1 } Under what circumstances t What is her sym- 
bol 1 Her color 1 How large does she appear 1 What is her mean solar distance, peri- 
odic time and the inclination of the plane of her orbit ? After the discovery of Pallai 
what did Dr. Olbers observe ? What hypothesis did he found upon this circumstance 1 
State why he thought it possible to dscover the other fragments and the method b» 
adopted for this purpose? 



VESTA — ASTREA. 227 

two points where the orbits of the three newly discov- 
ered planets mutually intersected, were in the constella- 
tions of the Virgin and the Whale, and in one of these 
two regions the supposed convulsion must have hap- 
pened, and through this place he conceived the frag- 
ments must still pass. 

502. Every month the astronomer examined the 
small stars in one or the other of these constellations. 
On the 29th of March, 1807, he beheld a star of the 
sixth or seventh magnitude in the constellation of the Vir- 
gin at a place where previous examination had shown 
that no star was visible. Upon the same evening he 
found that the object was really in motion, and continu- 
ing his observations until the 2nd of April, he became 
satisfied that this new object was in fact another planet. 
The name of Vesta was assigned it, and a flame burning 
upon an altar, in allusion to the peculiar rites of the god- 
dess is its appropriate emblem. 

503. Vesta is a small planet having a diameter of 
about 230 miles, yet when in opposition to the sun she 
appears the brightest of all the asteriods, and can be 
discerned without a telescope by a person of good eye- 
sight. A difference of opinion exists respecting the 
color of A r esta; some considering the planet to be of a 
ruddy tinge, others perfectly white, while to Mr. J. R. 
Hind, who has repeatedly examined it with glasses of 
various magnifying powers, it has always appeared of 
a pale yellowish hue. x 

504. The distance of Vesta from the sun is 216,467,- 
870 miles, and the period of her revolution 1,325 days. 
The plane of her orbit is inclined to that of the ecliptic 
7° 8' 25". 

ASTREA. (5) 

505. It was most confidently believed by many 
astronomers that other planets would be discovered, 
and Dr. Olbers continued his systematic search among 
the small stars in the constellation of the Virgin 
and the Whale, with unwearied assiduity until the year 

When did Dr. Olbers discover the fourth asteroid 1 State the circumstances attend- 
ing the discovery ? What name was assigned it .' What is the size of Vesta ? What 
i < her diameter '" Splendor '! (. olor ? Her mean solar distance, periodic time, inclin- 
ation of her orbit? Did Dr. Olbers detect any other planet .' 



228 SOLAR SYSTEM. 

1816 ; but no new planet was detected, and lie then 
abandoned his examination, regarding it as useless to 
continue it any longer. But all the members of this 
remarkable group of planetary bodies had not yet been 
discovered. 

506. Later Discoveries. On the 8th of December, 
1845, while Mr. Hencke of Driessen, was engaged in 
his astronomical labors, he perceived in the constel- 
lation of Taurus, a small star, that was not mapped 
down in an excellent star-chart which he was then 
comparing with the heavens. He at once conclud- 
ed that it was a new planet, and ere three weeks 
had elapsed its motion among the stars was fully 
established. At the request of the discoverer, the 
renowned astronomer, Encke, named the planet, which 
he called Astrea. 

Astrea shines with a faint light. She cannot be seen 
without a good telescope, for even under the most fa- 
vorable circumstances her brightness scarcely exceeds 
that of a star of the ninth magnitude. This planet is 
distant 237,000,000 miles from the sun, and revolves 
about it in 1,511 days. The inclination of the plane 
of its orbit to the ecliptic being 5° 19' 23". 

Mr. Hencke still continuing to compare his star-maps 
with the heavens, found on the 1st of July, 1847, a 
minute star neither marked down on his star-chart, nor 
seen by himself, on a previous examination of the heav- 
ens, in the place where he now saw it. Repeating his 
observations at midnight, on the 3d of July, he found 
it had changed its place among the stars ; he therefore 
pronounced it a planet, and before long it was recog- 
nized as such at all the principal observatories in 
Europe. The new asteroid was called Hebe. The in- 
clination of her orbit is 14° 46' 32"; distance from 
the sun 223,000,000 miles ; the period of her revolu- 
tion 1,379 days. 

How long did he continue his search? Why did he relinquish it? Give an ac- 
count of the later discoveries ? State when , by whom , and under what circumstances 
Astrea was discovered ? Describe Astrea? What is her solar distance, periodic time, 
and the inclination of her orbit ? State by whom, how, and when Hebe was discovered ? 



SIZE — ORBITS — PROBABLE NUMBER. 229 

Such was the beginning of a second series of brilliant 
asteroidal discoveries by various astronomers in dif- 
ferent parts of the world ; a series which is extending 
every year, although the number of asteroids is now 
(1870,) one hundred and ten. 

507. Peculiarities. The asteroids are distinguished 
from the earlier known planets by their small size, the 
great obliquity and eccentricity of their orbits, and by 
their being grouped together in a ring. 

508. Size. The planetoids are all, except Vesta, 
invisible to the naked eye, and through the telescope 
are distinguished from pale or fixed stars by their mo- 
tion. They are all very small bodies, Vesta being the 
largest. M. Argelander has constructed a formula by 
means of which the real diameters of fifty of the plan- 
etoids have been estimated. According to this com- 
putation their diameters vary from 260 to 15 miles, 
the smallest being so minute that a man could walk 
around it in a day. In brightness the asteroids range 
from the sixth to the thirteenth magnitude,. 

509. Obliquity and Eccentricity. The orbits of 
the asteroids are for the most part much more eccentric 
than those of the earlier known planets, and the incli- 
nation of the planes of their orbits to the ecliptic usu- 
ally greater. The inclination of that of Pallas being 
34° 37' 20". 

510. Orbits. The planetoids vary greatly in their 
distances from the sun. Flora, the nearest, being 
about 200,000,000 miles from that luminary, and 
Sylvia, the most remote, 320,000,000 miles ; their 
average solar distance being about 244,800,000 miles. 
The orbits of these bodies therefore constitute a sort 
of ring more than 100,000,000 miles in breadth, and 
they so interlace each other that if we imagine the or- 
bits to be rings of matter, no one of these rings could 
be lifted without taking all the rest with it. 

511. Probable Number op the Asteroids. The dis- 

What is the present number of the asteroids ? State their peculiarities ? What is 
said of their size? What of the obliquity and eccentricity of their orhif.s 9 What 
is stated respecting their solar distances and the complexity of their orbits ? 



230 SOLAR SYSTEM. 

tinguished astronomer, LeVerrier, lias estimated that 
the total mass of the group of asteroids between Mars 
and Jupiter may be equal to a third of the mass 
of the earth. The entire amount of matter com- 
prised in the 70 first-discovered asteroids has been com- 
puted to be no greater than about one ten-thousandth 
part of the mass of the globe. It may be therefore 
reasonably supposed that the asteroids belonging to 
this group are to be numbered by thousands. 

512. Origin op the Asteroids. According to the 
theory of Olbers, the asteroids have a common origin, 
being regarded as the fragments of a planet that once 
existed between Mars and Jupiter, but which was at 
length shivered by some mighty convulsion. If this 
is true, all the asteroids, in their orbitual revolutions, 
must pass through a common point, namely, the place 
occupied by the supposed planet at the time it was 
shattered. This theory possessed more probability 
while fewer planetoids were known, than at present, 
when so many have been revealed, since the orbits of 
these bodies by no means fulfill the above condition, 
for the orbit of the Flora, for instance, is distant from 
that of Sylvia by at least 50,000,000 miles. Accord- 
ing to the theory of Laplace, the planets have been 
formed from rings of nebulous matter thrown off from 
the sun, which were at length condensed into solid 
spherical masses, each ring usually condensing into a 
single planet. It is not improbable to suppose that a 
ring, instead of forming one planet, might have been 
broken up into numerous fragments, each of which 
would condense into a minute sphere, and thus from 
the ring a group of asteroids might be formed. 

According to the researches of LeVerrier, there ex- 
ists a ring of asteriods between the sun and Mercury, 
and a second at the distance of the earth from the sun, 
whose mass is equal to one-tenth of that of the earth. 

A table of all the asteroids which have been discov- 

What are LeVerrier's views in regard to the number of the asteroids ? What the- 
ories are held respecting their origin? Are there other groups beside those un- 
der consideration ? What is given in the Appeudix ? 



PHYSICAL ASPECT OP JUPITER — BELTS. 231 

ered up to the present time, (1870,) is given in the 
Appendix, (III,) including their navies, solar distances 
periodic times, dates of discovery, &c. 

JUPITER. % 

513. Periodic Time — Distance. Next in order 
from the sun is Jupiter, the most magnificent planet 
that illumines the sky. Its periodic time is 4,332 days, 
or somewhat less than twelve of our years. The mean 
distance of Jupiter is 477,017,781 miles, but owing to 
the eccentricity of his orbit this element is quite variable, 
for at his perihelion he approaches within 454,300,000 
miles of the sun, while at his aphelion he recedes to 
the distance of 499,700,000 miles from this luminary. 
The difference between these two distances is 45,400,- 
000 miles, an extent equal to one-half the solar dis- 
tance of the earth. 

514. Diameter — Apparent — Real. This planet for 
the reasons already given (Art. 177,) appears larger 
to us in opposition than in conjunction ; in the former 
position its apparent diameter measures 50 " and in the 
latter only 30". The real mean diameter is computed 
to be 87,501 miles. 

515. Ellipticity — Bulk. The ratio between the 
polar and equatorial diameters derived from the most 
recent measurements is as 947 to 1000 ; but Prof. 
Struve considers the inequality to be greater, being as 
85 to 92. Regarding the last ratio as correct, the 
polar diameter of Jupiter is less than the equatorial 
by nearly 7,000 miles, a quantity not quite equal to the 
diameter of the earth. The bulk of the planet is about 
thirteen hundred times greater than that of the earth. 

516. Physical Aspect op Jupiter — Belts. When 
this beautiful planet is seen through a telescope, no con- 
figurations are beheld on its surface, marking the posi- 
tions of continents and seas, as is the case of Mars, but 

What is the next planet in order from the sun 7 What is his periodic time ? His 
solar distance ? What is the difference between his perihelion and aphelion distances ? 
What is the magnitude of his apparent diameter * What the extent of his real diam- 
eter? What is said respecting the ellipticity and bulk of this planet? How does 
Jupiter appear when viewed through a telescope? 



232 SOLAR SYSTEM. 

dark hands termed belts are seen, stretching from side to 
side in the same direction. They are by no means uni- 
form in their appearance, and although for months they 
sometimes remained unchanged, they are yet liable to 
sudden and extensive, alterations in their breadth and 
situation, though not in respect to their general direction. 
In a few rare instances they have been seen broken up and 
distributed over the entire dish of the planet. Branches 
are frequently observed diverging from the main belts, 
and dark spots have likewise been noticed, of which as- 
tronomers have availed themselves to ascertain the 
period occupied by the planet in revolving on its axis. 

The views generally entertained by astronomers in 
respect to the cause of the belts are the following. It is 
supposed that Jupiter is surrounded by a luminous at- 
mospheric envelope, which conceals for the most part the 
planet itself, and that this bright canopy is parted by nar- 
row openings parallel to the equator of Jupiter. That an 
observer on the earth sees through these the dark surface 
of the planet, and that these glimpses of the solid body 
constitute the narrow dusky belts. The spectroscope re- 
veals the presence of water in the planet's atmosphere. 

517. These rents in the atmosphere of Jupiter, are sup 
posed to be caused by currents, like our trade winds, but 
vastly more powerful owing to the immense velocity 
with which the planet rotates, and the variations in the 
action of these winds upon the atmosphere of the planet 
would account for the changes that are noticed in the 
aspect of the belts. The appearance which Jupiter 
displays when seen through a telescope is shown in 
Fig. 74. 

518. Rotation. By observing a remarkable spot on 
Jupiter, Cassini, a distinguished Italian astronomer, as- 
certained in the year 1665, that this planet revolved 
upon its axis, completing a rotation in about 9h. 56m. 
Modern observations have established these conclusions, 
for the most able astronomers of the present day with 
the superior instruments they now possess, make the 

Describe the belts and their changes ? What is the cause of the belts ? What ex- 
ists in Jupiter's atmosphere? How are the changes in the appearance of the belts 
supposed to arise? At what time, and by whom, was the l-otation of Jupiter ascer- 
tained, and its period determined ? 



SATELLITES OF JUPITER — THEIR DISCOVERY. 233 
FIG. 74. 




JUPITER AND HIS BELTS. 



period of rotation very nearly the same. Mr. Airy the 
Astronomer Eoyal of England has fixed it at 9h. 55m. 
21sec., and Madler of Germany, at 9h. 55m. 30sec. 

519. Velocity of Rotation. The velocity with 
which this planet revolves on its axis is immense. In 
less than ten hours a particle on the surface of the planet 
at its equator sweeps through the whole extent of its 
circumference, or 274,889 miles. Its velocity there- 
fore exceeds 461 miles a minute, a speed twenty times 
greater than that of a cannon ball. 

520. Mass — Density. The quantity of matter in Ju- 
piter surpasses that of any of the other planets, and is 
to the mass of the sun in the ratio of 1 to about 980 ; 
in other words, the sun contains nearly nine hundred 
and eighty times as much matter as Jupiter. The density 
of this planet is about one-fourth that of the earth, ( T 2 /oths.) 

521. Satellites of Jupiter — their discovery. A 
splendid train of four moons or satellites is seen by the 
aid of the telescope, circling around this planet. They 
were discovered by Galileo of Padua, on the 8th of Jan- 
uary, 1610, and were the first fruits of his invention of 

■ — $ 

What is its period? What is said respecting the velocity of rotation? What of tha 
mass and densiiy of Jupiter! How many moons has Jupiter? By whom, when, ano 
how were they discovered 1 



234 SOLAR SYSTEM. 

the telescope. From that time to the present they have 
ever engaged the attention of astronomers, and their 
eclipses have been eminently serviceable in certain scien- 
tific investigations of which we shall soon speak. 

522. Their magnitudes — diameters — distances — 
and periods of revolution. No names have been 
given to these moons, but they are denominated the first, 
second, third, and fourth satellites, according to their distan- 
ces from Jupiter, the first being the nearest They shine 
as stars of between the sixth and seventh magnitude, but 
on account of their nearness to their brilliant primary, 
the telescope is needed to discern them. Their respec- 
tive diameters, distances, and periods of revolution around 
Jupiter, are given in the table below. 

DIAMETER. DI3T. FROM JUPITER. PERIODS OF REVOLUTION. 

First Satellite, 2,440 miles, 278,500 miles, Id. 18h. 27m. 34seo. 

Second, u 2,190 " 443,000 " 3d. 13h. 14m. 36seo. 

Third, " 3,580 " 707,000 " 7d. 3h. 42m. 33sec. 

Fourth, " 3,060 " 1,243,500 " 16d. 16h. 31m. 50sec. 

The first two satellites are larger than our moan, 
and the last two greater than the planet Mercury ; the 
diameter of the third exceeding that of Mercury by 630 
miles. 

523. Kepler's Laws — Eotation. The satellites in 
their respective distances from the planet Jupiter, and in 
their periodic times, obey the third law of Kepler — the 
squares of their periodic times being as the cubes of their 
distances from their common primary. An extended series 
of observations upon the periodical changes in their light 
led Sir William Herschel to infer, that each of the satel- 
lites revolves on its axis in exactly the same time as it 
completes one synodical revolution about Jupiter, thus 
following exactly the same law as our moon does in 
respect to the earth. 

524. The satellites as seen from the equator of Jupiter 
would present the following aopearances. The first 
would seem somewhat larger than our moon. The ap- 
parent diameters of the second and third would be about 

Why are they regarded with interest by astronomers 1 State their magnitudes, diame- 
ters, distances, and periodic times ? How do they compare in theH? actual dimensions 
with our moon and Mercury ? Does Kepler's third law apply to the satellites ? Stat* 
what is said in regard to their rotation 1 



TRANSITS AND ECLIPSES OF THE SATELLITES. 235 

two-thirds of that of the sun as viewed from the earth, 
while the apparent diameter of the fourth would be equal 
to one-quarter of that of the first. The planes of the 
orbits in which the satellites revolve, deviate but little 
from the plane of the planet's orbit, and as the apparent 
diameter of the sun as seen from Jupiter, is only about 
one-sixth of the apparent diameter of the first satel- 
lite, solar eclipses must be of common occurrence to the 
residents at Jupiter's equator, if any such residents 
there are. 

525. Transits and Eclipses of the Satellites. 
The satellites revolve about Jupiter from west to east, 
and in planes nearly coincident with each other. They 
are therefore seen ranging together in almost a straight 
line, and seem to move backwards and forwards in the 
heavens, now passing in front of the planet, and now 
behind it. 

526. When they pass before the planet their transits 
occur, and they cast shadows upon their primary which 
appear as dark spots crossing its bright disk. With pow- 
erful telescopes the satellites are occasionally seen as 
luminous spots, if projected on a dark belt; and at other 
times as dark spots of smaller size than their shadows — a 
circumstance which is accounted for by supposing that 
the satellites themselves have sometimes obscure spots of 
great extent, either on their own bodies or in their 
atmospheres. 

527. In passing behind the body of the planet or into 
its shadow at a distance from it, the satellites disappear 
and their eclipses occur. The three satellites which are 
nearest to Jupiter are totally eclipsed, every revolution 
around their primary, but the fourth, from the greater 
inclination of its orbit, sometimes escapes being eclipsed ; 
yet so seldom, that its eclipses may be regarded as hap- 
pening, for the most part, at every revolution like those 
of the others. 

What would be the respective apparent magnitudes of the satellites if seen from Jupiter's 
equntorial regions ? Why are solar eclipses of frequent occurrence at this planet? In 
what direction do the satellites revolve about Jupiter! Why are they seen in a straight 
line with each other? How do they appear to move in the heavens? When do thei/ 
transits- occur ? Describe them ? Why do the satellites sometime appear as dark spots 
on the disk of Jupiter ? Under what circumstances do their eeJpse* happen ? State wha 4 
it said of their frequency ? 



236 SOLAR SYSTEM. 

528. By the aid of these latter phenomena, astrono- 
mers have been enabled to construct tables of the mo- 
tions of the satellites, and likewise to determine approxi- 
mately the longitudes of places upon the earth. More- 
over, by their means the velocity of light has been ascer- 
tained. This discovery was made under the following 
circumstances. 

529. Velocity of Light. In the year 1675, Olaus 
Roomer, a Danish astronomer, noticed that if the calcu- 
lation of an eclipse of a satellite was made upon the sup- 
position that it would happen when Jupiter was in 
opposition, and the eclipse took place when the planet 
was in conjunction, that the actual time of the eclipse was 
later than the computed time by 16m. 26,6sec. On the 
contrary, if the calculation was made in view of Jupiter, 
being in conjunction, and the eclipse took place when he 
was in opposition, that then the actual time of the eclipse 
was earlier t\xm the predicted by 16m. 26,6sec. 

530. Now the difference of the distances of Jupiter 
from the earth when in conjunction and opposition is the 
diameter of the eart/i's orbit, or about 184,000,000 miles. 
This is evident from Fig. 75, where S represents the sun, 
E the earth, KO its orbit, JO 'J 1 the orbit of Jupiter, J 
the position of Jupiter in conjunction, and J 1 at opposi- 
tion. Now the distance of Jupiter from the earth at 
conjunction is equal to Jupiter's solar distance (JS,) added 
to the earth's solar distance (ES,) but at opposition it is 
equal to Jupiter's solar distance (J'S,) diminished by the 
earth's solar distance (ES.) The difference in the dis- 
tances of Jupiter from the earth, at opposition and con- 
junction is therefore equal to twice the earth's distance 
from the sun (EO,) or nearly 184,000,000 miles. 

531. Roemer suspected that the difference between 
the actual and predicted times of an eclipse, was owing 
to the circumstance that the light from the satellite had to 
travel farther in coming to the earth, when the planet was 
in conjunction than when in opposition, and it was there- 
fore inferred that light passed through the space of 

In wlmt particulars have these phenomena subserved the interests of srienre ? State 
when, and by whom the velocity of lijr/it wits ascertained? (iive u full account of tint 
discovery, explaining from Figure. 




VELOCITY OF LIGHT. 



184,000,000 miles in 16m. 26.6s., or nearly 186,500 
mites per second. 1 This conclusion has been established, 
for two other independent modes of computing the velocity 
of light have since been discovered, both of which give 
substantially the same result as is afforded by the first. 

532. The most ancient observation of Jupiter on 
record was made at Alexandria, on the 3rd of Septem- 
ber, 240 years before Christ, when the planet was seen to 
eclipse a certain star in the constellation of the Crab 



SATURN. ^ 

533. The next planet is Saturn ; a vast globe inferior 
in magnitude only to Jupiter, but surpassing it in the 
wondrous structure of its system, for Saturn is attended 
by a train of no less than eight satellites and is girdled by 
several rings of stupendous size. 

1. Tli* velocity per second is obtained by dividing 184,000,000 miles 
by 16m. 26,6sec. reduced to seconds. In 16m. 26,0sec, there are 986,6see., 
dividing 184,000,000 miles by this number we obtain as a quotient 186,500 
miles, which is the velocity of light per second. 

What is the velocity of light per second as obtained by Roemer 1 Is this computation 
correct ? Why ? What is the most ancient observation of Jupiter on record 1 What 
planet is next discussed 7 What is said of its grandeur 1 



238 solar system. 

534. Distance — Periodical Kevolution and In- 
clination of Orbit. The mean solar distance of Sat- 
urn, is 874,581,498 miles, but on account of the eccentri- 
city of his orbit, he is distant from the sun at his aphe- 
lion 923,200,000 miles, and at his perihelion 826,000,000 
miles. The solar distance of the planet thus varies more 
than 97 ,200, 000 miles. The time employed by Saturn in 
making one siderial revolution is 29 \ years. The inclina- 
tion of the plane of its orbit to that of the ecliptic is 2° 
29 / 36". 

535. Form and Diameter. From an extended 
course of observations Sir William Herschel was of opin- 
ion, that the disk of Saturn differed in form from that 
of the other planets of our system ; for instead of being 
oval, it seemed an oblong or parallelogram with the 
corners rounded off. This view was generally adopted 
by astronomers until a series of actual measurements, 
made by Prof. Bessel of Konigsberg, and Mr. Main of the 
Koyal Observatory of England, revealed the error, and 
proved that the disk of Saturn does not deviate sensibly 
from an ellipse. The form of the planet is therefore 
spheroidal. According to Prof. Bessel, the ratio of the 
equatorial diameter of Saturn to the polar is as 1000 to 
903. The mean diameter of the planet is 74,568 miles, 
the difference between the polar and equatorial diam- 
eters, computed from the preceding ratio will conse- 
quently be 7,600, an extent nearly equal to the diam- 
eter of the earth. 

536. Bulk — Density — Intensity of Light. Saturn 
is nearly one thousand times larger than the earth. 
His density is but one-ninth that of our planet (^V^hs), 
therefore, nine cubic feet of Saturn, would on an aver- 
age, contain the same amount of matter as one cubic 
foot of our globe. The intensity of the solar light at 
Saturn is 90 times less than it is at the earth. 

537. Physical Aspect — Atmosphere. Saturn ap 
p»;ars of a pale yellowish hue, and when viewed through a 
good telescope belts are frequently seen upon its surface, 

Tell of its solar distance, periodic time, and of the inclination of the plane of its orbit / 
Sta.e whnt is snitl in regard to its form ? What is the true form of the ph.net 1 What is the 
ratio of the equatorial to the polar dinmetcr nf Saturn according to Prof. Bessel ? What 
their re<pectivt> lengths in mile;! ? How -jrcnt is their difference ? Ftnte what is snid re 
ipecting the b Ik and density of Sutum ? What in regurd to h's degree of illumination » 



RING OF SATURN — ITS DISCOVERY. 239 

but far more faint and obscure than those which are re- 
vealed upon the disk of Jupiter. Spots are rarely 
noticed on this planet. 

538. The changes in the number and appearances of 
the belts, led Sir William Herschel to think, that Saturn 
is enveloped in an atmosphere of great density. In this 
opinion he was strengthened by the circumstance, that 
when the nearest satellites of Saturn in the course of their 
revolutions passed behind the planet, they seemed, as 
they approached and receded from its edge, to remain 
upon it too long ; the satellite which is closest to the 
planet lingering twenty minutes behind its computed 
time, and the next fifteen. This detention was only to 
be accounted for by the refraction of the light of the sat- 
ellite through an atmosphere surrounding Saturn. 

539. About the polar regions of this planet, Herschel 
repeatedly observed recurring changes in its light, and 
the appearance of extensive cloudy spaces, which in- 
creased the evidence of the existence of a dense atmos- 
phere. The spectroscope has recently shown that it 
contains water. 

540. ROTATION AND INCLINATION OF ITS AXIS. In 

1793, Sir William Herschel instituted a most diligent 
and thorough observation of the belts, for the purpose of 
determining the time of the rotation of Saturn. He 
watched and noted them with great care through one 
hundred rotations, examining them under varied circum- 
stances and aspects, and at length came to the conclusion 
that Saturn completes a revolution on his axis in lOh. 
16m. 4sec. ; a result which Herschel was certain could not 
deviate from the truth by so much as two minutes. The 
axis upon which Saturn revolves is inclined to the plane 
of its orbit 63° 10', a position which tends to give to the 
planet nearly the same diversity of seasons as that which 
our earth enjoys. 

541. Ring of Saturn — its discovery. When Gali- 
leo in the year 1610, directed his telescope to Saturn, the 
figure of the planet appeared so singular, that he thought 

Describe the physical aspects of this planet? What led Herschel to believe that 
Saturn possessed a dense atmosphere ? Does it contain water ? State by whom and 
in what manner its rotation was ascertained ? What is the period of rotation as de- 
termined by Herschel ? Is it exactly correct ? What is the inclination of the axis 
of rotation to the plane of its orbit ? What is saii of the seasons of this planet ? 

11 



240 SOLAR SYSTEM. 

it consisted of a large globe with a smaller one on each 
side. About 50 years afterwards Huyghens, a distin- 
guished Dutch philosopher, observed Saturn with tele- 
scopes of greater magnifying power than those which 
had been employed by Galileo, and soon made the dis- 
covery that the planet was surrounded by a vast lumin- 
ous ring, unconnected with the body of the planet. 

542. When the telescope had been still farther im 
proved, and instruments of higher magnifying powers 
and finer construction were at command, two English 
gentlemen of the name of Ball, in October, of the year 
1665, first noticed that the ring was double ; a phenome- 
non which was observed by Cassini at Paris, 1675, and 
to whom the honor of this second discovery is usually 
attributed. Of the later discoveries mention will be made 
in a succeeding article. At present while discussing cer 
tain particulars respecting this wonderful appendage, 
we shall speak of it as one ring. 

543. Form — Constitution. The ring may be de- 
scribed as circular, broad, and fiat, like a coin with a 
round central opening. Like the planet it shines by the 
reflected rays of the sun and has usually been supposed 

by astronomers to consist of solid matter. Some as- 
tronomers believe that the ring is fluid. If, however, 
we regard it as composed of a vast number of separate 
bodies, the various appearances which it presents can be 
readily accounted for. For where the bodies are closely 
aggregated, the ring will appear bright; where sparsely 
collected, dim; and if the bodies are gathered into sep- 
arate circular groups, divisions in the ring will occur. 

544. Eotation — Position — Inclination to the 
Ecliptic. From the observations made upon certain 
spots on its surface, Sir William Herschel inferred that 
the ring rotated in its own plane in the space of lOh. 
32m. 15sec. ; a period precisely the same as that which 
La Place proved it ought to have, according to the theory 
of universal gravitation. The plane of the ring is ex- 
actly coincident with the plane of the planet's equator and 
is inclined to the ecliptic at an angle of 28° 10 / 27". 

(Jive an account of the discovery of Saturn's ring ? What is so id respecting "\s forth 
4iid constitution ? What of its rotation, position, and inclination f 



PHASES OF THE RING. 



241 



545. Phases of the King. When viewed through 
a telescope at considerable intervals of time the ring of 
Saturn presents different aspects. For at one time it 
appears broad zmdflat and of an elliptical shape, with an 
open space between it and the planet, while at another 
it is narrowed down and looks like two handles project- 
ing from each side of the planet ; and then again it van- 
ishes entirely from our sight. 

546. The causes of these changes are found in the fol- 
lowing facts ; First, that the ring, like the earttis axis, 
always remains parallel to itself, and Secondly, that we 
view it in different positions at different times. 

547. This subject is illustrated in Fig. 76, where the 



FIG. 76. 




SATURN AND HIS RING. 



carve abed, represents the orbit of the earth, the central 
figure the sun and A, B, C, D, E, F, Gr, H, eight positions 
of Saturn in his orbit. Now if we were stationed upon 
the sun, Saturn being at C, the solar light falling upon 
the flat surface of the ring would be reflected back to 
us, and we should see the ring in its greatest breadth ; the 
opening between the planet and the ring, would likewise 
be readily discerned. But as the planet in its orbitual 
motion advanced to D, the visible portion of the ring 
would contract, since we should now view its surface 
more obliquely than we did at first. 

548. When Saturn had arrived at E, where the plane 
of tlw ring passes through the suni the solar rays would 
fall only on the edges of the ring, which is so thin that 
the reflected light would be too faint to render it visible. 

Describe the phases of the ring ? Illustrate hy the lid of Figure; 76 



242 SOLAR SYSTEM. 

In this position the ring consequently woul 1 vanish from 
our sight. As the planet advanced successively to F 
and G, the visible surface of the ring would gradually in- 
crease, attaining at Gr the same apparent breadth and 
exhibiting the same aspect as it possessed at C. Sat- 
urn continuing his progress to A, would once more 
contract in size, becoming invisible at A where its plane 
passes again through the sun. From A to C, the ap- 
parent surface of the ring would gradually increase re- 
gaining at C its original breadth and appearance. 

549. In the above illustration we have discussed the 
phases presented by the ring as viewed from the sun, but 
our point of sight is the eartt situated somewhere in 
the orbit abed. This circumstance modifies somewhat 
the appearance of the ring as explained above, but not 
to any very great extent, for the earth is so much nearer 
the sun than Saturn is, that the ring exhibits to us 
almost exactly the same aspects as if we actually beheld 
it from the sun. 

550. Vanishing of the Ring — Three causes. Our 
position upon the earth multiplies however the causes 
of the disappearance of the ring. Since it appears to us 
very nearly as it would to a spectator upon the solar orb, 
we in the first place lose sight of it when its plane passes 
through the sun ; unless telescopes of the greatest power 
and finest construction are employed, when a faint line 
of light is just perceived marking the position of the ring. 
In the second place the ring vanishes when its plane passes 
through the centre of the earth, for then its edge only is di- 
rected to us which does not reflect light enough to 
become visible. Lastly, when the plane of the ring passes 
between the earth and the sun, it disappears from our sight, 
because the side which is illumined by the sun's rays is 
then turned from us, and the dark side presented towards 
us. Thus in the figure, such would be the case if 
the earth was somewhere between c and d, while Satnrr 
was a little distance from E moving towards F, yet not 

Does Saturn and his ring appear nearly the same from the earth as it would from the 
iun ? State the three causes of the disappearance of the ring, and explain why the ring 
will vanish when it is in any one of these three positions 1 Can the ring be discerned in 
any way when its plane passes through the sun 1 



DIVISIONS OF THE RING. 243 

so far from E but that the plane of the ring would pass 
between the earth and the sun. l 

551. Divisions of the Ring. We have already al- 
luded to the discovery made by the Messrs. Ball, and also 
by Cassini, that the ring of Saturn is double. For nearly 
a century, astronomers have been led to think from the 
appearance of dark lines upon the ring that other subdi- 
visions exist, and these surmises have proved correct. 

552. In 1837, Prof. Encke of Berlin, saw through the 
famous telescope of Fraunhofer, the outer ring of Sat- 
urn divided by a black line and so clearly denned that he 
was enabled to take the measurements of its breadth. 
This separating line was observed some years afterwards 
by Messrs. Lassel, Dawes, and Hind, and also by Prof. 
Challis of Cambridge University, England, and with such 
marked distinctness as to leave no doubt of the actual 
division of the outer ring. 

553. But this discovery was soon followed by another 
still more surprising, which was no less than the detec- 
tion of a dusky obscure ring, nearer to the planet than 
what is usually termed the bright inner ring. On the 
11th of November, 1850, Mr. Gr. P. Bond, of Harvard 
University, saw such evidences of subdivision in the 
inner ring as led him to infer that a third ring existed 
nearer the planet and less bright than the other two. 
On the 29th of the same month, the Rev. W. R. Dawes, 
of Wateringbury, England, made the same discovery, 
and noticed likewise the additional fact that the dusky 
ring is itself double ; being divided by an extremely fine 
line. 



1. Mr. J. R. Hind, in 1852, thus described the phases of Saturn's ring. 
" In 1848, after the north surface had been visible for nearly 15 years, the 
ring became invisible on April 22d, when the earth was in the plane of the 
ring ; it reappeared on the 3d of Sept., when the sun was so situated in 
respect to the ring as to illumine the southern surface, which was turned 
towards us. On the 12th of the same month, the earth passed to the 
northern side of the ring, while the sun still shone on the southern side, 
and the ring consequently disappeared a second time. It continued in- 
visible to us until the 18th of January, 1849, when the earth passed to the 
southern side of the ring which had been turned towards the sun since the 
3d of September, 1848. We shall continue to see the southern surface of 
the ring until the close ot the year 1861." 

Relate in full the discoveries that have been made in respect to the divisions of the ngl 



244 SOLAR SYSTEM 

554. What therefore was at first regarded as a single. 
ring is now found to consist of five ; viz., two obscure 
rings nearest the planet, and three bright ones beyond 
them. The two exterior luminous rings constitute what 
has hitherto been termed the outer ring of Saturn, and 
the third the inner ring. Fig. 77, represents Saturn and 

FIG. 77. 




SATURN ..8 VIEWED BY THE REV. W. R. DAWES, ON NOVEMBER 29TH, 1850. 

his rings as they appeared to Mr. Dawes of Watering- 
bury, when viewed through a telescope of the finest 
construction. The division of the dark inner ring is 
however not delineated. 

555. Dimensions of the Rings. The dimensions of 
the outer and inner 1 rings of Saturn have been deter- 
mined by the most accurate and careful measurements 
to be as follows : 

From the surface of the planet to the inner edge of ) , PCt0 ., 

foe first bright ring, . . . } l8 ' 628 mile8 ' 

Breadth of the inner ring, 16,755 " 

Breadth of the interval between the bright inner and ) , „ f . <:> u 

outer ring, \ ^'^ 

Breadth of the outer ring, 10,316 " 

Outer diameter of the outer ring, 172,130 " 

1. Outer and inner ring. By the outer ring is here meant as stated 
in the preceding article, the two exterior bright rings. The inner ring is 
the third bright ring, next to the dark one. 

How many rings have been found ? fiive the dimensions of the outer and inner rings of 
Saturn t 



SATELLITES OF SATURN. 245 

5t>6. The thickness of the rings has been estimated by 
Sir John Herschel, at not more than 100 miles, while 
Mr. G. P. Bond, of Cambridge, places the thickness as 
low as 40 miles. 

557. Satellites of Saturn. Saturn is attended by 
eight moons, seven of which revolve about the planet 
in orbits, whose planes are nearly coincident with that 
of the ring. They have received the names of Mimas, 
Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, and 
Japetus. 

558. On account of their great distance from the earth 
these bodies, although possessed of considerable size, are 
only visible by the aid of powerful telescopes. We shall 
describe them briefly, commencing with the one nearest 
to Saturn, and taking them in the order of their distan- 
ces from the planet. 

559. Mimas. This satellite was discovered by Sir 
William Herschel, on the 17th of September, 1789, with 
his immense reflecting telescope of 40 feet focal length. 
The largest instruments and the most favorable circum- 
stances are needed to see this moon merely as a small 
bright point. Such is the extreme difficulty of detecting 
it, that few astronomers have even beheld it. The mean 
distance of Mimas from the centre of Saturn is 118,000 
miles, and it revolves about the planet in 22h. 36m. 
18sec. It is distant from the ring about 32,000 miles. 

560. Enceladus. On the 19th of August, 1787, Sir 
William Herschel first noticed this satellite, before his 
great telescope was completed. The discovery was con- 
firmed by the aid of this noble instrument in August, 
1789. Enceladus has been observed by Sir John Her- 
schel several times, shining like a star of the fifteenth 
magnitude. It revolves about Saturn in Id. 8h. 53m. 
7sec, and its distance from the centre of the planet is 
152,000 miles. The plane of its orbit according to Sir 
William Herschel's observations is coincident with that 
of the ring. 

561. Tethys. This satellite was found by Cassini 

What is the thickness of the rings according to Sir John Herschel? What according 
to Mr. G. P. Bond? How many moons has Saturn? Whut is the position of the planes 
of the orbits of seven ? Give the names of the satellites ? What is said as to their visibility 1 
State in full what is said of Mimas, and Enceladus ? 



246 SOLAR SYSTEM. 

in March, 1684. It resembles a star of the thirteenth 
magnitude, and performs its revolution around Saturn 
in an orbit the plane of which is nearly if not exactly 
coincident with that of the ring. It completes a revolu- 
tion around its primary in the space of Id. 21h. 18m. 
26sec, at the distance of 188,000 miles from the centre 
of the latter. 

562. Dione. Dione was likewise discovered by Cas- 
sini, in March, 1684. In size it varies between the 
eleventh and twelfth magnitude, and its distance from the 
centre of Saturn, is equal to that of our moon from the 
earth, being 240,000 miles. Dione revolves in an orbit 
supposed to be coincident with that of the plane of 
the ring and performs its revolution in 2d. 17h. 44m. 
51sec. 

563. Rhea. Cassini detected this moon of Saturn 
on the 23d of December, 1672. It shines usually like a 
star of the tenth or eleventh magnitude, but at times, ap- 
pears as one of the ninth, and then again of the twelfth 
magnitude ; its brightness depending much on its posi- 
tion in respect to Saturn, and also on the state of our at- 
mosphere. The plane of the orbit of this satellite, 
nearly coincides with that of the ring. Rhea revolves 
about its primary in 4d. 12h. 25m. Usee, and is distant 
836,000 miles from its centre. 

564. Titan. This is the largest of all the satellites of 
Saturn, and shines as a star of the eighth magnitude. 1 1 
was discovered by Huyghens, on the 25th of Maivh, 
1655, and has recently been studied with great care by 
Prof Bessel. Titan revolves about Saturn at the distance 
of 778,000 miles from its centre, performing a revolution 
in the space of 15d. 22h. 41m. 25sec. 

B65. Hyperion. This satellite was discovered as late 
as September, 1848, and almost at the same time by two 
observers. Mr. G. P. Bond, of Harvard University, 
detected it on the 16th of September, and Mr. Lassol, of 
Liverpool, on the 18th of the same month. 

Hyperion appeared to Prof. Bond, as a star of the 
seventeenth magnitude. Its distance from Saturn and 

Give an account of T*thys t Dione, Rhea, Titan, Hyperion. 



DIAMETERS OF THE SATELLITES. 247 

period of revolution have not yet been very accurately de 
termined, the former however, is not far from 940,000 
miles, and the latter 21d. 4h. 20m. ' 

566. Japetus. This is the most remote of all the sat- 
ellites of Saturn. Its distance from the centre of its pri- 
mary is no less than 2,268,000 miles, and its period of 
revolution 79d. 7h. 54m. 41sec. The plane of the orbit 
of this satellite is inclined to that of the ring about 10°. 
Japetus, was discovered by Cassini, towards the close of 
the month of October, in the year 1671. Periodical 
changes in the light of this satellite have been noticed, 
which lead to the inference that it revolves on its axis in 
the same time that it completes a revolution around 
Saturn, just as our moon does in respect to the earth — 
a law of revolution which probably exists in the case 
of all the satellites belonging to the planets of our 
system. 

567. Diameters of the Satellites. Of these meas- 
urements we have little knowledge. Prof. Struve has 
reckoned the diameter of Titan, the largest, to be 3,800 
miles, which is regarded as not far from the truth. 
Schroeter estimated the diameter of Titan at 2,850 miles, 
that of Japetus at 1,800 miles, of Ehea 1,200, and the di- 
ameter of Dione and Tethys at 500 each. Sir William 
Herschel supposed Mimas to be 1000 miles in diameter. 

568. Sir John Herschel has detected a singular rela- 
tion between the periods of revolution of the four interior 
satellites ; viz., that the periodic time of Mimas is one-half 
that of Tethys, and the period of Enceladus, one-half that 
of Dione. The rotation is almost mathematically exact. 
The laws of Kepler, hold true in regard to Saturn's sat- 
ellites, as well as in the case of Jupiter's. 

569. Ancient observations of Saturn. The most 
ancient observation of Saturn on record, was made by 
the Chaldeans, on the 1st of March, 228 vears before 
Christ. On the 21st of February, 503 A.D., the planet 
was seen at Athens, apparently emerging from behind 
the moon. 



Give an account of Japetus ? What is said respecting the diameters of the satellites ? 
What singular relation has been noticed by Sir John Herschel 1 What is here said in re- 
•pect to the application of Kepler's laws ? What ancient observations have been recorded 
sf Satu n ? 



248 SOLAR SYSTEM. 

URANUS, OR HERSCHEL. IJt 

570. Until the year 1781, all the known planets, ex- 
cluding our earth, were Mercury, Venus, Mars, Jupiter, 
and Saturn. Each of these, more or less conspicuous to 
the unaided eye, had been recognized as planets for ages, 
but about this time, Sir William Herschel, having con- 
structed telescopes of great power, commenced a sys- 
tematic examination of the heavens, which led to the 
most surprising discoveries. 

571. On the 13th of March, 1781, between ten and 
eleven o'clock, this eminent astronomer detected an 
object which he at first suspected to be a comet, but sub- 
sequent observations established its planetary nature. 
The new planet was called by Herschel Georgium Sidus, 
as a compliment to his patron, George III., and by 
others, Herschel in honor of the discoverer; but the 
name proposed by Bode of Uranus, is now universally 
adopted. 

572. Aspect — Diameter — Mass — Density. Ura- 
nus appears of a pale color, uniformly bright, and unde- 
versified with spots, belts, or configurations of surface such 
as are seen on Jupiter and Mars. Its diameter is about 
33,294 miles, and like other planets it is probably ellipti- 
cal inform, having its equatorial diameter longer than its 
polar. This difference has not yet been satisfactorily es- 
tablished. Prof. Madler thinks he has detected it, and 
makes the ratio of the equatorial diameter to the polar 
to be as 10 to 9. But other astronomers, with telescopes 
of greater power, have been unable to discern any differ- 
ence at all in the lengths of the various diameters of the 
planet. According to the recent calculations of Mr. 
Adams, the sun contains about 21,000 times as much 
matter as Uranus. The density of Uranus, according 
to LeVerrier, is -jVfrths of that of the earth. 

573. EOTATION. The absence of spots and outlines 
upon the unvarying bright surface of Uranus, deprives 
astronomers of the means of determining the period of 
its rotation. In fact whether it revolves at all upon its 

When was Uranus discovered, and by whom? What are the various names of this 
planet t S'-ate what i.< said in regard to its aspect, diameter, 7iia.;s, and density ? 



SATELLITES 01 URANUS. 249 

axis is a point not yet fully determined, but as it belongs 
to a system of planets, all the rest of which revolve on their 
axes, it is reasonable to infer from analogy that Uranus 
also does. 

574. Distance — Inclination of orbit — Periodic 
Time. The average distance of Uranus from the sun is 
1,758,753,228 miles, his least distance 1,675,000,000 
miles, and his greatest 1,842,500,000 miles. Thus on 
account of the eccentricity of its orbit, the difference 
between the perihelion and aphelion distances of the 
planet is no less than 167,500,000 miles — an extent 
nearly twice as great as the distance of the earth from 
the sun. The plane of the orbit of Uranus almost coin- 
cides with that of the ecliptic, for its inclination is less 
than 47'. Uranus revolves about the sun in 30686.8 
days, a little more than 84 of our years. 

575. Satellites of Uranus. Uranus was found by 
Sir William Herschel to be attended by six satellites, but 
notwithstanding the zealous efforts of astronomers, little 
certain knowledge has yet been gained in respect to 
their elements. 

576. The second and fourth satellites, in the order of 
distance from the planet, are those that are best known ; 
the periodical revolution of the former, being according 
to the computations of Mr. Adams, 1 8d. 16h. 56m. 25sec, 
and that of the latter, 13d. llh. 6m. 55sec. Uranus 
every year is becoming more and more favorably sit- 
uated for observation, and there is every reason for be- 
lieving that our knowledge of this planet will ere long 
be more complete than it is at present. 

577. The satellites of Uranus differ in two particulars 
from all the other planetary bodies that compose the solar 
system. For all the planets and their satellites, except- 
ing those of Uranus, revolve in their orbits from west to 
cast, and the planes of their orbits do not deviate far from the 
plane of the ecliptic ; but the attendants of Uranus move 

1. The computations of Mr. Adams, are the most recent and are con- 
sidered the most correct. 

What of its relation, distance, inclination of orbit and periodic time ? How many 
natellites has Uranus ? What do w3 know respecting thern ? Pave they any peculiarities ' 
What are they 1 



250 SOLAR SYSTEM. 

around the planet from east to west, and the planes of their 
orbits are nearly perpendicular to the plane of the ecliptic, 
being inclined to it at an angle of 78° 58 / . 

578. Intensity of Light. Since Uranus is about 
19 times as far from the sun as the earth is, the intensity 
of the solar light is here diminished in the ratio of 1 x 1 
to 19 x 19 (361.) In other words the intensity is 361 times 
less at Uranus than it is at the earth. 

NEPTUNE. 

579. History of its Discovery. When an astron 
omer knows perfectly all the elements of a planet, he 
can tell at what time it will be in a particular place in 
the heavens, with greater precision than the station-mas- 
ter of a rail-road can tell when a certain train will arrive 
at a given station. If the planet does not arrive at its ap- 
pointed place at the computed time, it must be owing to some 
influence unknown to the astronomer, provided he has made 
no error in his calculations. Now Uranus, ever since 
its discovery, has not kept its appointments, for astrono- 
mers have been constantly finding it in a different place 
from that in which it ought to have been according to 
their calculations. It was always off the track, and they 
at length suspected that these deviations were caused by 
the attraction of a planet hitherto undiscovered. 

580. Mr. Adams of St. John's College, Cambridge, in 
1843, and Mr. Le Verrier, of Paris, in 1845, unknown to 
each other, undertook the task of solving this intricate 
problem, calculating how large a planet would account 
for these deviations, what distance it must be from the 
sun, what orbit it must have, and various other particu- 
lars. In September, 1846, the French astronomer had 
so fully completed his computations, that on the 23d of 
the month, he wrote to Dr. Galle, of Berlin, telling him 
where to look in the heavens for the unknown planet and 
of what size it would appear. Dr. Galle, the same eve- 
ning he received the letter, pointed his instrument to 
that region in the heavens where he had been directed 

How intense is the solar light of Uranus 7 What is^he next plunet in order 7 Give the 
history of the discovery of Neptune 7 



HAS NEPTUNE A RING. 251 

to gaze, and there he immediately saw a sta^ of the mag- 
nitude mentioned by Le Verrier, and which proved to 
be the planet sought. 

581. Name — Diameter — Mass — Density. The 
planet of Le Verrier has generally received from astron- 
omers the name of Neptune. 1 Its diameter deduced from 
measurements made with the best instruments of 
Europe is 35,797 miles. Its mass, according to Le 
Verrier, is about twenty-jive and a half times that of the 
earth, and the sun contains about 13,000 times more 
matter than Neptune. The density of this planet is 
estimated to be nearly three times that of Saturn, ov 
about one-third of the density of the earth. 

582. Orbit — Inclination of orbit — Distance — 
Periodic time. The most accurate determination of 
Neptune's orbit was made by Mr. Sears C. Walker, of 
Philadelphia. Like that of the other planets it is ellip- 
tical, yet but moderately so, and its plane is inclined to 
that of the ecliptic 1° 47'. The mean solar distance is 
2, 753,661, 884 miles, and the difference between its greatest 
and least distance from the sun is 48,260,000 miles, an 
extent considerably less than one-third of the like varia- 
tion of Uranus. Neptune revolves about the sun in 
60126.72 days, or about 164| years. 

583. Intensity of Light. As this planet is about 
30 times farther from the sun than the earth is, the in- 
tensity of the solar light at Neptune, is 900 (30 x 30) 
times less than it is at the earth. 

584. Has Neptune a King. Mr. Lassel, of Liver- 
pool, and Prof. Challis, of Cambridge, England, have at 
various times supposed that they saw traces of a ring sur- 
rounding the planet. Prof. Bond, of Cambridge, has fre- 
quently noticed a luminous appendage, but not so defined 

1. Several names were proposed for this planet, Dr. Galle wished to 
to call it Janus. Other astronomers, Le Verrier, after the eminent mathe- 
matician whose profound researches led to its discovery, but the name of 
Neptune has been adopted by most astronomers, and approved of by M. 
Le Verrier himself. 

What is said respecting the name of this planet in the text, and note? What of its 
diameter, mass, and density ? What is said of the orbit of Neptune and its inclination f 
What of his solar distance and periodic time ? What is the intensity of solar light at 
Neptune compared with that at the earth ? 



252 SOLAR SYSTEM. 

as to enable him to announce the existence of a ring. 
Other able astronomers, with some of the best iastru* 
ments at command, have not even detected any pecu- 
liarity in the aspect of the planet, which would lead 
them to suspect that it was encircled by a ring. 

585. The Satellite of Neptune. In about a month 
after the discovery of Neptune by Dr. Galle, Mr. Las- 
sel, of Liverpool, detected a satellite, shining like a star 
of ike fourteenth magnitude. From all the observations 
made by this astronomer, and others, up to the end of the 
year 1848, it appears, that the satellite revolves about 
Neptune in an orbit nearly circular, that it completes a 
revolution about its»primary in 5d. 21h., and at the mean 
distance from the latter of 232,000 miles. This moon 
of Neptune is at about the same distance from the planet 
as our moon from the earth ; and Mr. Lassel discovered 
the interesting fact, that there are such periodical 
changes in its brightness, as to indicate that this sat- 
ellite like others belonging to our system, rotates 
on its axis in the same time that it revolves around 
Neptune. 

586. Mr. Bond, of Cambridge, believes that he has ob- 
tained tolerably good evidence of the existence of a 
second satellite, more dim and distant than the first, but 
not enough to enable him as yet to pronounce decidedly 
upon it. The fact that the more remote planets are at- 
tended by trains of satellites, and the singular unresolved 
appearance observed near Neptune, by the English and 
American astronomers, render it not improbable that an 
assemblage of moons may be at length found, circling 
around this far distant member of our system. 

REAL AND APPARENT MOTIONS OF THE PLANETS. 

587. A spectator upon the sun would see all the. 
planets revolving with beautiful precision around this 
luminary from west to east, and constantly pursuing the 
same direction. Such are the real motions of the planets 
in their orbits. A person upon the earth, sees only the 

Hns Neptune tiring? Give an account of the satellite of Neptune ? Is the existence 
of a second moon suspected ? May Neptune possibly have many satellites 1 State what 
is meant by the real motions of a planet ? 



APPARENT MOTIONS EXPLAINED. 253 

apparent motions of these bodies, which differ so widely 
from their real motions, that a superficial observer might 
imagine that they actually ivandered in the heavens, and 
were guided by no law. For at one time we behold a 
planet pursuing its direct course from west to east, after a 
while it becomes stationary, and then in a short time it 
resumes its motion, moving in a retrograde course from 
east to west. 

588. The apparent motions of the inferior planets are 
quite complicated, and vary in some respects from those 
of the superior planets on account of their different posi- 
tions in regard to the earth — the former having an inferior 
conjunction and no opposition, and the latter an opposition 
and no inferior conjunction. 

589. Causes of the Apparent Motions. The ap- 
parent motions of the planets are owing to two causes. 
First, that we behold them from a stand-point above 95,- 
000,000 miles from their centre of motion, and conse- 
quently see them in a different quarter of the heavens 
from that in which they would appear, if seen from the 
sun. Secondly, the earth is not stationary, and when we 
observe the planets, we assign to them the motion that 
belongs to the globe on which we stand, since we are 
unconscious that it moves at all. 

590. Apparent motions explained. Selecting one 
of the superior planets, we will now endeavor to explain 
why its apparent motions differ so much from its real 
Let Jupiter be that planet, and suppose him to be on 
the other side of the sun, in superior conjunction. He 
will then be seen to move in the same direction as the 
earth, that is from west to east, and as we are uncon- 
scious of our own motion, the apparent motion of Jupi- 
ter will equal his own real motion added to that of the 
earth. When Jupiter is near opposition, the planet and 
the earth are moving as it were on parallel tracks, with 
the starry heavens beyond Jupiter ; but the earth moves 
faster than Jupiter, and at length goes by him, and as 
our globe seems stationary to us, Jupiter is seen to 

What by its apparent motions ? Why do the apparent motions differ so much from th» 
real motious 1 What nre the causes of the apparent motions? Explain wny the appa 
rent motions of Jupiter are at one time direct and at another retrograde ? 



254 SOLAR SYSTEM. 

move backward, among the stars, from east to west. 
The retrograde motion of an inferior planet occurs 
near its inferior conjunction. 

591. Thus if two boats are sailing down a river, one 
of which is in the middle, and the other near the shore; 
if the former sails faster than the latter, a spectator upon 
the first will see the other boat apparently moving up the 
stream, though they are both really proceeding in the 
same direction. 

592. The Planets at times Stationary. We have 
just shown that in one part of a planet's orbit, its appa- 
rent motion is direct, and in another retrograde. There 
must accordingly be points in its orbit where its ap- 
parent motion changes from direct to retrograde, or the 
contrary ; and at these points the planet must necessarily 
for a while appear stationary. Mercury is stationary at 
the distance of about 15° or 20° from the sun, and 
Yenus at 29°. 



CHAPTER VI. 

COMETS. 



593. Comets area class of bodies belonging to the 
solar system entirely different in appearance from any 
we have yet considered. The orbits in which they 
revolve are so elliptical, that during the greater part 
of their circuit they are invisible, being only detected 
when near the sun. 

594. Constitution. The comet, when entire, consists 
of three parts; the head, or nucleus — the coma, or 
envelope, and the tail. The head is nearest to the 
sun, and appears as a bright spot more dense than the 
other portions ; but whether it consist of solid matter, 
like a planet is yet undetermined, for no telescope has 

Give the illustration in respect to the retrograde motion ? Explain why the planeti are 
Ht times stationary ? At whnt angular distance from the sun is Mercury stationary 1 At 
wliirt distance Venus? What does Chapter VI. treat of? What is said respecting Mies* 
b(«die»? Of how many parts doe* a cvimpt consist? 



NUMBER OF COMETS. 255 

ever jet revealed a true round dish in any comet. Sur- 
rounding the head, but yet perhaps separated from it, is 
the coma which is a luminous fog-like covering that 
probably conceals from our view the real body of the 
comet. This envelope is conceived to give to comets a 
hairy appearance, hence their name. 1 

595. The tail is an expansion of the coma, the light 
matter of which streaming backward on either side in a 
direction opposite to the sun, diffuses itself for the most 
part into two broad trains of light, extending to an im- 
mense distance, and which constitute the tail. These 
streams sometimes unite at a short distance behind the 
head, and at others continue distinct throughout most of 
their length. All comets do not possess tails, even some 
of the most conspicuous present to view tails of only 
moderate dimensions, while others are as perfectly free 
from them as a planet. On the other hand, in a few 
instances, the tail has been divided into more than two 
streams, as in the case of the comet of 1744, when this 
extraordinary appendage was seen spreading out like a 
fan into six magnificent trains. 

596. The tails of comets are often curved outward in 
the direction in which the body is proceeding. These 
appendages increase in length and splendor as they ap- 
proach the sun until they are lost from view in his bril- 
liant rays. Upon emerging into sight on the other side 
of the sun, the comet attains its greatest brightness, and 
the tail, now extended to its utmost limit, shines forth 
in full splendor. As the comet departs from the sun, 
the tail gradually loses its radiance, and decreases in 
length till it is absorbed in the head. 

597. In Fig. 78, where the comet of 1819, is delin- 
eated, its three distinct parts are easily recognized. 

598. Number of Comets. This class of celestial 
bodies is without doubt very numerous, for, according to 
Sir John Herschel, the list of those on record before the 
invention of the telescope amounts to several hundred. 

1. Comet from the Greek home, signifying hair. 

Describe each of them in full? Do all comets possess tails or trains? Does a comet 
ever have more than one ? State the changet to which these appendages are subject ? 
What is said respecting the number of comets on record before the telescope was invented 1 

12 



256 



SOLAR SYSTEM. 
FIG 78. 




COMET OF 1819. 

The telescope has added materially to this number, tor 
not a year passes without some being brought to light 
from the depths of that obscurity in which they must 
have forever remained, if the astronomer had continued 
to gaze upon the heavens with his unaided eye. Within 
the last century, more than 140 comets have been seen 
which have not yet made their second appearance. 

599. Thirty comets are known to have their perihelion 
distances within the orbit of Mercury, and M. Arago basing 
his calculations upon this fact, and also upon the suppo- 
sition that comets are uniformly distributed through 
space, has computed that 3,529,470 comets have their 
perihelion distances within the orbit of Uranus. Moreover 
since comets may come within the limits of our solar 
system and yet be invisible to us, even with the telescope 
in consequence of daylight, the prevalence of fogs and 
chuds, and also from their being within the circle of per- 
petual occultation, M. Arago has considered, that he might 
safely estimate the number of comets within the orbit 
of Uranus at 7,000,000. If this calculation is extended 

Has this instrument aided astronomers very much in this field of research ? How many 
liave been noticed within the last century which have not made their second appeaiance? 
State Arago's computation of the number of comets? Extend this computation to the orbit 
of Neitune ? 



VELOCITY. 257 

as tar as Neptune, the number of comets whose 'perihel- 
ion distances are within the orbit of this planet would 
amount to more than 28,000,000. 

600. Splendor and Size. Comets vary much in 
respect to their brilliancy and magnitude; for while 
multitudes are only visible through the telescope, many 
of which are destitute of tails and heads, appearing 
only as cloudy star; others almost dazzle the gaze 
with their brightness, and extend their bright tails half 
across the heavens. Some comets have been seen of 
such surpassing splendor that they were visible in clear 
daylight, such were the comets of 1402 and 1532, and 
also that of 1843. 

601. The famous comet of 1680 was conspicuous for 
the great length of its tail ; for soon after its nearest ap- 
proach to the sun, this wondrous appendage shot out 
from the body of the comet to the distance of 60,000,000 
miles, and in the incredible short space of two days. 
When it had attained its greatest length it extended no 
less than 123,000,000 miles from the head, covering a 
space in the heavens greater than the distance from the 
horizon to the zenith. The comet of 1811, had a nucleus 
only 428 miles in diameter, while the tail stretched out 
to the distance of 108,000,000 miles. The diameter of 
the envelope of the comet of 1843, was 36,000 miles, 
and the greatest length of the train 108,000,000 miles, 
a length more than 4000 times the circumference of the 
earth. 

602. Velocity. Comets when nearest the sun, move 
with incredible speed, that of 1680, is said to have gone 
half around the sun, in ten and a half hours, moving 
with the speed of 880,000 miles an hour, or more than 
645 times faster than a cannon ball. The comet of 1843, 
sweeping more than half around the sun in two and a 
half hours moved with a velocity of 1,300,000 miles an 
hour, or one forty fourth as fast as a message is trans- 
mitted through the wires of the telegraph. As these 

State what is said in regard to the splendor and size of these bodies? State what 
is here said of the several magnitudes of the comets of 1680, 1811, and 1843 1 What is re- 
marked of the velocity of comets when nearest the sun"? Give an account of the speed 
of the comet of 1680. and of that of 1843 ? What is said respecting the velocity of » 
notnet as it departs from the sun ? 



258 SOLAR SYSTEM. 

bodies depart from the sun, their velocity decreases, ac- 
cording to the laws of attraction already explained, 
(Art. 405,) and to describe those portions of their respec- 
tive orbits that are remote from the sun, requires periods 
of time, varying from a few years to many hundreds. 

603. Temperature. The temperature of comets de- 
pends upon their proximity to the sun, since like the 
planets they derive their light and heat from this source. 
The comets most remarkable for their close approach to 
the sun are those just mentioned ; viz., the comets of 1680 
and 1843. The first was only 147,000 miles from the 
surface of the sun, and was exposed to a heat 27,500 
times greater than that received by the earth in the 
same time — a heat 2,000 times greater than that of red-hot 
iron and sufficient to turn into vapor every known ter- 
restrial substance. At this distance the sun, as it would 
have appeared from the comet, must have had an appa- 
rent diameter more than 140 times greater than it has at 
the earth, and would have covered a space in the heav- 
ens extending from the horizon to near the zenith. 

604. The comet of 1843, came within about 60,000 
miles of the sun's surface ; so near in comparison with the 
immense distance it recedes from the sun that it is said 
to have almost grazed it. The sun as viewed from this 
comet at its 'perihelion would have had an apparent di- 
ameter of 121° 32', and its disk would have appeared 
forty-seven thousand times larger than it does at the earth. 

605. According to Sir John Herschel, the heat it re- 
ceived from the sun was 47,000 times greater than that 
which falls upon the earth in the same time, when the 
*un is shining perpendicularly upon it. So intense is 
such a heat that it is 24^ times greater than that which is 
sufficient to melt agate, and rock crystal. The comet even 
for some days after it passed its perihelion, presented a 
glowing appearance, being in fact red-hot. 

606. Comets shine by reflected Light. This fact 
is proved in the following manner, when a self-luminous 

From what source do these bodies derive their light and heat? What comets are re- 
markable for their near approach to the sun 1 How near did the comet of 1680 approach 
the surface of the sun ? How hot was it? Why was it so hot ? How large would the 
sun appear if viewed at the perihelion distance of this comet ? State the like particulars 
respecting the comet of 1843 1 



ORBITS — PERIHELION DISTANCES. 259 

body, as a lamp for instance, is carried gradually away 
from us, the size of the flame grows smaller as the dis 
tance increases, while the brightness is the same at all dis- 
tances. But if a body which shines by reflected light is 
thus withdrawn, it grows fainter andfaintei; until at last 
it vanishes. 

607. Now when comets are subjected to this test, it is 
found that their brightness is not the same at all distan- 
ces, but that it gradually diminishes as they recede from 
us. These bodies shine then by reflected light, the bright 
beams of the sun reflected from their diffused atoms of 
matter, causing the enormous volume of the comet to glow 
with light ; in the same manner as the flying vapors that 

# float in our atmosphere become radiant throughout 
their whole depths, with the reflected solar beams. 

608. Orbits— Perihelion distances. The orbits of 
comets for the most part are ellipses, with the sun in 
their common focus; but unlike those of the planets 
which deviate but little from a circle in form, the ellip- 
tical orbits of comets are exceedingly elongated, their 
major axes (Art. 16,) running out to almost an infinite 
length. 

609. In consequence of this extended form of the 
orbit, the comet is only beheld for a short time while it 
is near the sun ; after which it occupies years and even 

. centuries in accomplishing the remainder of its circuit — ■ 
sweeping far beyond the limits of the planetary system 
where no telescope can begin to descry it. 

610. The perihelion distances of these bodies are very 
various, l 30 are found to approach nearer the sun than 
Mercury, and most of those visible' from the earth have 
swept nearer to the sun than Mars. Others have doubt- 
less their perihelion distances far more remote, but are 
unseen by us on account of their great distances. In a 
very few instances comets have been known to move in 
hyperbolas, a curve that does not return into itself;* These 

1. See Figure 1, page 16. 

2. A curve is said to return into itself, when a body starting from 
any point of it, and moving along it, at last comes round to the same 

Do comets shine by their own or bv reflected light ? Prove it 1 State what u said re- 
specting the orbits of comet* and their perihelion distances "* 



260 SOLAR SYSTEM. 

therefore sweeping around the sun can never again re- 
visit us while the nature of their path remains un- 
changed ; but speed away to unknown systems, or wan 
der through the limitless regions of space, till they come 
within the influence of some vast orb strong enough to 
control their roving propensities. 

611. Inclination of their orbits — Direction of 
Motion. The orbits of comets differ also from those of 
the planets in respect to position; for while those of the 
latter have in general but a small inclination to the 
plane of the ecliptic, the orbits of the former cut it at all 
angles, being sometimes nearly perpendicular to it. 
Neither have comets like the planets a common motion 
from west to east, but they traverse the heavens in all- 
directions, subject to no law in this particular. 

612. Out of nearly 200 comets whose respective direc- 
tions are known, about one-half have a retrograde, and 
the other a direct motion. 

613. Elements — Identity. Three good observa- 
tions of the right ascension and declination of a comet, 
together with the times at which they were made, are 
sufficient to enable the astronomer to calculate the ele- 
ments of its orbit. l Of all the comets that have been 



point again. Such curves are the circle and ellipse. The curve of the 
hyperbola is shown in the annexed Figure, B is the vertex of the curve, 




and from this point it stretches away in two branches BA and BC to an 
infinite length, the branches continually diverging from each other. A 
body n oving along this curve from any point of it can therefore never 
return to the place whence it started. This curve does not return into 
itself. 

1. The elements of a comet's orbit are, 

1. The longitude of the perihelion. 

2. The longitude of the ascending node. 

3. The inclination of the plane of its orbit to that of the ecliptie. 

What of the inclination of their orbits an d direction of motion ? How many and 
what observations will enable an astronomer to compute the elements of a comet's orbit « 



halley's comet. 261 

observed the orbits of about 190 have been determined, 
and out of all these, the return of only four have been 
verified by observation; namely, Halley's, Encke's, 
Biela's, and Faye's. 

614. The identity of a comet upon its return is estab- 
lished by the identity of its elements, and not by its physi- 
cal appearance, for this is subject to change; the body 
presenting great modifications in this respect upon its 
successive returns. 

615. Halley's Comet. Edmund Halley, a celebrated 
English astronomer, upon calculating the elements of 
different comets, discovered that the elements of the 
comets of 1531, 1607, and 1682 were identical. He there- 
fore concluded that these three comets, so called, were 
actually one and the same body, which revisited the 
earth at these epochs. The interval between 1531, and 
1607, being 76 years, and that between 1607 and 1682, 
being 75 years, he ventured to foretell that the comet 
would reappear in nearly 75 or 76 years from the last 
date, and accordinglv predicted its return about the 
year 1759. 

616. Clairaut, an eminent French mathematician, 
after calculating the amount of the influence of Saturn 
and Jupiter in retarding the appearance of the comet, 
fixed the time of its return to its perihelion, within a 
month, one way or the other, of the middle of April, 
1759. It came on the 12th of March in that year. 

617. In the year 1835 it again returned, passing its 
perihelion within one day of the time calculated by Pon- 
tecoulant, a French astronomer. So vast and eccentric 
is the orbit described by this comet, that while its peri- 
helion distance is 57,000,000 miles, its aphelion distance is 
3,420,000,000 miles, a point in space more remote than 
that of Neptune, by 600,000,000 miles. 

618. Halley's comet had been observed and its pecu- 

4. The eccentricity of the orbit. 

5. The length of the semi-major axis of the orbit 

6. The time of passing the perihelion. 

7. Motion, whether direct or retrograde. 

Of how many have the orbits been computed 1 What number of comets have had then 
returns verified by observation ? Mention them? How is the identity of a comet estab 
1 1 Give the full account of Halley's comet ? 



262 SOLAR SYSTEM. 

liarities recorded four times before its appearance m 1682. 
In 1305, it is described by the writers of that age as a 
comet of a dreadful size. In 1456, its train extended 
through the heavens for the space of 90°, stretching from 
the horizon to the zenith, and filled all Europe with such 
terror that, by the decree of the Pope, prayers were of- 
fered in all the Catholic churches, and the bells rung at 
midday in order to avert the wrath of heaven. In 1682, 
the tail was only 30° in length ; in 1759, it had so di- 
minished in size that it was not visible to the naked eye 
until it had passed its perihelion, while in 1835 its tail 
was about 20° in length. 

619. Encke's Comet. This comet receives its name 
from Prof. Encke, of Berlin, who first ascertained that it 
returned at stated times, in the short period of 1,211 
days, or about 3^ years. Prof. Encke made this dis- 
covery upon its fourth recorded appearance in 1819, and 
predicted its return in 1822. It came at the appointed 
time, and from that year forward it has returned at its 
regular intervals, obeying the same law of gravitation 
that controls the earth in her orbit. 

620. Biela's Comet. This is another small cometary 
body which revolves about the sun in the period of 
2,410 days, or about 6f years. This discovery was 
made by Mr. Biela, of Josephstadt, in the year 1826, 
who predicted the return of the comet in 1832. The pre- 
diction was fulfilled. In 1839, its position was very un- 
favorable for observation, and there is no record of its 
having been observed at all at this time. 

621. Upon its return in the year 1846, this body was 
most surprisingly modified, for instead of one comet it 
was separated into two bodies, each having the true 
characteristics of a comet. These twin bodies, which 
were termed the comet and its companion, passed along 
through the heavens side by side for the space of 70°, 
changing in their relative brightness and magnitude, and 
also in their distances from each other. 

622. According to Mr. Plantamour of Geneva, the 
distance between the nucleus of the comet, and that of its 

Give tfae full account of Encke's, of Biela's ? 



comet op 1680. 263 

companion, during the time of their visibility varied 
from 149,000 miles to 154,000 miles. 

623. F aye's Comet. Mr. Fay e of Paris, discovered 
Nov. 22, 1843, a telescopic comet which has a period of 
about 7 J years. The return of the comet to its perihe- 
lion was predicted to take place within a day or two of 
April 3, 1851. It was seen by Prof. Challis of Cam- 
bridge, England, Nov. 28, 1850, and reached its peri- 
helion within a day of the predicted time. The peri- 
helion distance of this comet is 161,000,000 miles. 

624. Brorsen's Comet. Mr. Brorsen, of Denmark, 
in 1846, discovered a comet which has a period of 
about 5 -J years. It was seen on its return to its peri- 
helion in 1857, at which time it was 62,000,000 miles 
from the sun. 

625. D'Arrest's Comet. In 1851, D'Arrest, of Leip- 
sic, discovered a comet having a period of about 6.4 
years. It returned to its perihelion at the time pre- 
dicted, in November, 1857, at which time it was 111,- 
000,000 miles from the sun. 

626. Winnecke's Comet. In 1858, Dr. Winnecke, 
of Bonn, rediscovered a comet at its seventh revolution 
since 1819, when it had first been noticed, and whose 
periodic time had been computed at about h\ years. 
Its perihelion distance is 73,000,000 miles. 

These six comets of short periods resemble each other 
in the direction of their motion, and in the eccentric- 
ity, dimensions, and inclination of the planes of their 
orbits to the ecliptic. 

627. Comet of 1680. This comet is supposed to 
revolve about the sun in a period of 575 years. 

628. It is regarded as identical with a comet which 
was beheld at Constantinople, in the year 1105, A.D., 
with one that was seen close to the sun in the year 575 
A. D., with a third which appeared in the year 43 B.C. : 
and lastly, with two others mentioned in the Sybilline 
Oracles, and in Homer. 

Give the full account of Fay e's Comet Of Brorsen's. Of D' Arrest's. Of Win- 
necke's. What is said of the six comets of short periods ? State what is further 
said of the comet of 1680. 

12 



264 SOLAR SYSTEM. 

629. Comet of 1843. We have already stated many 
particulars respecting this most extraordinary body, but 
a further description is by no means superfluous. It 
was seen on the 28th of February, 1843, close to the sun, 
its brightness being so great that the splendor of the solar 
beams could not overpower its brilliancy. 

630. "In New England," says Professor Loomis "it was-i 
beheld from half past 7 A.M., till 3 P.M., when the sky 
became considerably obscured by clouds. The appear- 
ance was that of a luminous globular body ; the head of 
the comet, as observed by the naked eye appearing cir- 
cular ; its light equal to that of the moon at midnight in 
a clear sky, and its apparent size about }th the area of 
the full moon." 

631. At the Cape of Good Hope, it was seen by every 
person on board the Owen Grlendower, on the day just 
mentioned, at about sunset, near the sun, and having the 
shape of a dagger. 

632. The vast extent of the tail has already been 
stated. At the Cape of Grood Hope, it appeared on the 
3rd of March to be double, two trains diverging from the 
head in a straight line, forming a small angle with each 
other. Near the equator this magnificent appendage 
shone with such a glow that at times it threw a bright 
light upon the sea. The comet remained visible only for 
a short time, the earliest observation upon it appears to 
have been made on the 27th of February, and the latest 
on the 15th of April. 

633. The elements of this comet are not yet decidedly 
ascertained. A brilliant comet appeared in 1668, the 
head of which was concealed by the splendor of the 
solar rays, and whose tail, extending to an immense dis- 
tance, was so vivid that its image was reflected from 
the surface of the sea. The investigations of astrono- 
mers point in their results to an identity between the 
comets of 1668 and 1843 ; inasmuch as on the whole, 
they present nearly similar aspects, pursue nearly the 
same path, and the period of revolution assigned to 
each is 175 years. Prof. Hubbard, of the Washington 
Observatory, finds however, from a rigorous discussion 

Describe in full the comet of 1843? 



COLLISION WITH THE EARTH. 265 

of all the observations made on the comet of 1843, that 
it most probably revolves in an elliptical orbit, in a 
period of about 170 years. 

634. Physical nature of Comets. These extraor- 
dinary bodies consist of matter, but existing in an at- 
tenuated and diffused state, of which we have no ade- 
quate conception. That they consist of matter is proved 
by the fact that they revolve in regular orbits around the 
sun, obeying the same law of attraction as the solid 
masses of the planets ; and that this matter is extremely 
rare and subtile, is shown by the circumstance that the 
smallest stars are visible through the tail of a comet. 

635. A light cloud, in comparison with the matter 
composing the tail of a comet, is to be regarded as a dense 
and heavy body. For while the former, though gauze-like 
in its texture and of moderate thickness is yet sufficiently 
dense to obscure the light of a star ; the latter, notwith- 
standing it is millions of miles in extent, permits the stel- 
lar rays to traverse its vast thickness, and to reach the 
eye, distinctly revealing the orb from which they ema- 
nate. 

636 The amount of matter in comets, even of the 
largest size, is so small that their passage around the sun 
has never in the least perceptible degree affected the 
stability of the solar system ; in other words, they have 
never, as far as could be perceived, caused the planets to 
deviate a hair's breadth from their accustomed paths 
around the sun. 

637. According to the celebrated La Place, if the mass 
of the comet of 1770, which passed within 1,500,000 
miles of our globe, had been equal to that of the earth, 
it would have increased our sidereal year by 2h. 53'. But 
the profound investigations of Delambre, showed that the 
length of the year was not increased by the fraction of 
a second, and that consequently the mass of the comet, 
could not have been equal to one-five thousandth part of 
the mass of the earth. 

638. Collision with the Earth. Fears have often 

State what is said respecting the physical nature of comets 1 Show that the matter of 
comets must be very much attenuated ? Why must their amount of matter be small 1 
Give the proof? 



266 SOLAR SYSTEM. 

been entertained that collisions might occur between 
the earth and comets. When any one of these bodies 
has its perihelion within the orbit of Mercury it must 
necessarily cross the orbits of all the planets, and such 
a collision may possibly take place, but the probability 
is exceedingly small. 

639. Upon the supposition that the nucleus of a comet 
possesses a diameter one-fourth the size of that of the 
earth, and that its perihelion is within the earth's orbit, 
Arago has computed the chance of our meeting the 
comet to be as 1 to 281,000,000. 

640. But were the earth to meet a comet, it would be 
somewhat like a cannon ball meeting a cloud, and the 
earth would probably suffer but little from the encoun- 
ter. Indeed, it has been supposed by some, that we 
have already passed through the tail of a comet without 
knowing it, for, according to Mrs. Somerville, there is 
reason to think that such was the case when the great 
comet of 1843 revealed its splendors to our eyes. 



CHAPTER VII. 



METEORIC BODIES. 



641. Shooting Stars. Shooting stars, or meteors, 
are small luminous bodies that are seen darting nois- 
lessly through the sky, followed by a bright train, and at 
times attended by dazzling coruscations of varied hues. 
Solitary shooting stars may be seen every clear night, 
but at certain periods these bodies occur in such numbers 
that they cannot be counted, and present the phenom- 
enon of a star shower. 

642. Height and Telocity. By means of simulta- 
neous observations made at two or more stations, 
considerable distances apart, the height and velocity 

Is is possible for a comet to strike the earth? Is it probable? What effect -won Id 
a collision with a comet probably have upon the earth? May we have already pas.«c I 
through the tail of a comet? "What does Chapter VII treat of? What are shooting 
stars ? Are they frequent ? What occurs at certain periods ? 



STAR-SHOWERS. 267 

of these bodies can be easily found. In order to in- 
vestigate these points, as well as others, Brandes and 
Benzenberg, two German philosophers, made a series 
of simultaneous observations in the fall of the year 
1798. On six evenings, between September and No- 
vember, 402 shooting-stars were beheld, and of these 
twenty-two were so identified that their altitudes, at the 
moment of their extinction, could be readily computed. 
The least and greatest elevations were si» miles and 
one hundred and forty. 

643. In 1823, the investigation was renewed by 
Brandes, at Breslau and the neighboring towns, on a 
more extended scale. Between April and October, 1800 
shooting-stars were seen at the different stations. Out 
of this number, 98 were observed simultaneously at 
more than one station, and afforded the means of esti- 
mating their respective altitudes. The least and high- 
est elevations were 15 miles and 460 miles. 

644. Similar observations were made in Switzerland, 
on the 10th of August, 1838, by Wartman and others. 
A part of the observers stationed themselves at Geneva, 
and the rest at Planchettes, a village about sixty miles 
to the north-east of that city. In the space of seven 
hours and a half, 381 shooting- stars were seen at 
Geneva, and in five hours and a half 104 at Plan- 
chettes. All the circumstances attending their ap- 
pearance were carefully noted, and their average height 
was computed &tfive hundred and fifty miles. 

645. As regards velocity, in the first series of ob- 
servations made by Brandes and Benzenberg, only two 
shooting-stars afforded the means of determining their 
speed; one possessed a velocity of 1500 miles per 
minute, and that of the other was between 1020 and 
1260 miles per minute. 

646. In the second series, undertaken in 1823, the 
estimated rate of motion varied between 1080 and 
2160 miles per minute. At Belgium, in 1824, M. 

What is said respecting their height and velocity ? 



268 SOLAR SYSTEM. 

Quetelet obtained observations upon six of these sin- 
gular bodies, from which he was enabled to deduce 
their respective velocities, which were found to range 
from 600 to 1500 miles a minute. 

647. How they are Inflamed. The immense ve- 
locity with which shooting stars enter our atmosphere 
causes such a condensation of the air that heat is de- 
veloped of a sufficiently high -intensity to inflame them. 
Upon the supposition that these bodies compress the 
rarefied atmosphere, at the height of 35 miles above 
the earth, to the density of common air, the intensity of 
the heat developed would be 46.080° Fah., nearly three 
times greater than the highest temperature of a glass 
furnace. No shooting star, or any portion of it, has 
ever been known to reach the earth. These bodies are 
therefore, probably, of a gaseous nature, and are en- 
tirely consumed in their passage through air. 

648. Meteoric Showers. At certain epochs meteoric 
displays occur of surpassing splendor. The most noted 
of these epochs are those of the 12th and 13th of No- 
vember, and the 9th and 10th of August. 

649. On the morning of the 12th of November, 1799, 
an extraordinary display of this nature was seen by 
Humboldt and Bonpland,atCumana,in South America. 
During the space of four hours the sky was illumined 
with thousands of shooting-stars, mingled with meteors 
of vast magnitude. This phenomenon was not con- 
fined to Cumana, but extended from Brazil to Green- 
land, and as far east as Weimar, in Germany. 

650. On the 13th of the same month, in 1831, a 
meteoric shower occurred at Ohio, and also near Car- 
thagena, off the coast of Spain. At the latter place, 
luminous meteors of large size were beheld, one of 
which left behind it an enormous train, tinted with 
prismatic hues, its track continuing visible for the space 
of six minutes. On the same day of the following 
year, vast numbers of shooting-stars fell at Mocha on 

How are they inflamed ? Can sufficient heat be produced by their motion to in- 
flame them ? Have shooting stars ever been known to reach the earth ? 



al t gust epoch. 269 

the Red Sea, upon the Atlantic ocean, and in Switzer- 
land. The same brilliant spectacle then appeared in 
various parts of England ; the sky being illumined 
soon after midnight by the rushing of thousands of 
meteors in every direction. 

651. But by far the most magnificent display of this 
kind occurred on the night of the 12th and morning 
of the 13th of November, 1833. It extended from the 
northern lakes to the south of Jamaica, and from 61° 
W. Long, in the Atlantic, to about 150° W. Long, on 
the Pacific ocean near the equator. For the space of 
seven hours, from 9 P. M. to 4 A. M., the heavens 
blazed with an incessant discharge of fiery meteors, 
that burst in countless numbers from the cloudless sky. 
At times they appeared as thick as snow-flakes falling 
through the air, as large and as brilliant as the stars 
themselves ; and it required no vivid imagination to 
suppose that these celestial bodies were then actually 
rushing toward the earth. It was estimated that at 
this time no less than 240,000 meteors fell. 

652. In 1868 an extraordinary star-shower occurred 
at this period throughout the United States. At New 
Haven, Ct., 7,359 were observed within the space of 
six hours. 

653. The November meteors appear to emanate from 
a certain region in the heavens, situated in the constel- 
lation Leo. 

654. The August epoch was first distinctly announced 
by Thomas Foster of London, in 1827, and every year 
an unusual display of meteors occurs at this period ; 
the number being five times the average of the year. 
Like the November meteors those of August seem to 
radiate from a small space in the heavens situated 
in the constellation Perseus. Meteors are also un- 
usually abundant on the 21st of April and the 7th of 
December. 

Give an account of meteoric showers. From what constellation do the November 
meteors appear to emanate? What is said of the August epoch? From what con- 
stellation do the August meteors seem to radiate ? 



270 SOLAR SYSTEM. 



METEORITES AND AEROLITES. 

i 655. Meteorites. Besides those meteoric bodies 
which are probably of a gaseous nature, there are oth- 
ers that are undoubtedly solid ; these are termed 
meteorites. They appear as fiery bodies, sweeping 
through the atmosphere with immense velocity, and 
attended by a luminous train. During their progress 
explosions frequently occur, by which fragments are 
detached and fall to the earth, while the meteorite 
usually passes onward in its course. These fragments 
are termed aerolites. In rare instances the aerolite 
consists of the entire meteoric body. 

656. The Weston Meteorite. At half past six 
o'clock, on the morning of the 14th of Dec, 1807, a 
meteorite was seen rushing from north to south, over 
Weston, in the State of Connecticut ; its apparent di- 
ameter being equal to one-half, or two-thirds, that of 
the full moon. As it passed behind the clouds, it ap- 
peared like the sun through a mist, and shone with a 
mild and subdued light ; but when it shot across the 
intervals of clear sky, the glowing body flashed and 
sparkled like a firebrand carried against the wind. 
Behind it streamed a pale, luminous train, tapering in 
form, and ten or twelve times as long as its diameter. 

657. The meteorite was visible for the space of half 
a minute, and just as it vanished gave three, distinct 
hounds. About thirty seconds after its disappearance, 
three heavy explosions were heard like the reports of a 
cannon, succeeded by a loud, whizzing noise. Directly 
after the explosions, a person of the name of Prince 
heard a sound resembling that occasioned by the fall 
of a heavy body, and upon going from the house per- 
ceived a fresh hole in the turf, at the distance of 
twenty-five feet from the door. At the bottom of the 
hole, two feet below the surface, an aerolite was dis- 
covered which weighed nearly 35 pounds. 

What are meteorites ? "What phenomena attend their appearance ? What are the 
frauments termed ? Give an account of the Weston meteorite ? 



AEROLITES. 271 

658. Another mass, which was dashed to pieces upon 
a rock, was judged, from the fragments collected, to 
have weighed two hundred pounds. Other aerolites 
fell in various parts of the town. The stones, at the 
time of their descent, were hot and crumbling, but 
gradually hardened upon exposure to the air. 

659. The Ohio Meteorite. On the 1st of May, 
1860, a meteorite passed over North-western Virginia 
and South-eastern Ohio. It appeared as a blazing ball 
of fire, was followed by a brilliant train of light, and 
exploded with a tremendous noise, which was heard 
over an area 150 miles broad. At New Concord, 
in Muskingum County, a loud report was first heard 
like that of a cannon, which was followed, at intervals 
of a few seconds, by twenty-three distinct detonations, 
when the sounds became blended together, and re- 
sembled the roar of a railway train. After these 
explosions a large number of stony fragments fell 
throughout an area ten miles long and three miles wide. 
The largest fragment which was discovered weighed 
one hundred and three pounds, and descended with such 
force that it penetrated the earth to the depth of nearly 
three feet. This aerolite is now in the cabinet of Mari- 
etta College. 

660. Height and Velocity of Meteorites. Mete- 
orites vanish at the height of about 32 miles above the 
earth, but their altitudes range from 15 to over 90 
miles. Their velocity is about 19 miles a second, 
equal to that of the earth in its orbit. 

661. Size of Meteorites. The diameter of the 
Weston meteorite was computed to be 300 feet, and 
that of the meteorite observed by Mr. Cavallo, at 
Windsor, on the 18th of Aug., 1783, was calculated 
by this gentleman to be no less than 3,210 feet, or 
more than three-fifths of a mile. Mrs. Somerville men- 
tions one that was estimated to weigh nearly 600,000 
tons. 

Give an account of the Ohio meteorite ? What is said in regard to the height 
and velocity of meteorites? What of their size 1 



272 SOLAR SYSTEM. 

662. Aerolites. The greater number of aerolites, 
according to Schreibers, have always the same general 
form, which is that of an oblique or slanting pyramid. 
They are also alike in external appearance, presenting 
to view a black, shining crust, as if the body had been 
coated with pitch. This crust is not greater than the 
two-hundredth part of an inch in thickness, its com- 
position is identical with that of the mass, it bears the 
marks of fusion, and strikes fire with the flint. When 
broken, the surface of the fracture displays the color 
of an ash-grey. 

663. "Distinct aerolites," says Berzelius, the cele- 
brated chemist, "are frequently so like one another in 
color and external appearance, that we might believe 
them to have been struck out of one piece." 

664. Aerolites are composed of about twenty of the 
sixty-three elementary substances which are found in 
terrestial matter, iron and silex being predominant. 

665. They contain no new element, but the combin- 
ation of those of which they consist is so peculiar, that 
aerolites are readily distinguished from all terrestial 
bodies. Their density is from 3 J to 4J times greater 
than that of water. In some cases the aerolite con- 
sists almost entirely of iron. 

666. An instance of this kind occurred May 26th, 
1751, when a meteorite burst with a tremendous ex- 
plosion over Hradschina, in Upper Sclavonia. Two 
fragments were seen rushing to the earth, the largest 
of which struck deep into the ground. It weighed 
71 lbs., and consisted of 95.5 per cent, of iron and 3.5 
per cent, of nickel. A portion of the iron being polish- 
ed and corroded with acids, a most beautiful crystalline 
structure was revealed. 

667. Meteoric Iron. From the peculiar constitu- 
tion and structure of aerolites, we are enabled to de- 
tect the meteoric origin of masses of iron which are 

Give the general form of the aerolite ? What is said of their crust ? Of what 
do aerolites consist ? In what are they peculiar ? What is their density ? Do they 
ever consist almost entirely of iron ? Give an account of the aerolite of Hrads- 
china? State what is said respecting meteoric iron? 



THEORY IN REGARD TO METEORIC BODIES. 273 

found scattered over the surface of the earth, but which 
were never seen to fall from the sky. 

668. Humboldt relates that there is an enormous 
mass of iron near Durango, in Mexico, which posses- 
ses exactly the same composition as the aerolite of 
Hradschina. 

669. In the cabinet of Yale College is a mass of 
meteoric iron which was found in Texas in the year 
1808. Its weight is 1,635 lbs. 

670. Theory in regard to Meteoric Bodies. The 
observations which have been made upon meteoric 
bodies, prove that they revolve about the sun in ex- 
tended elliptical orbits like those of comets. The inter- 
planetary spaces are, therefore, according to this view, 
not to be regarded as vacant, but as occupied to a great 
extent with innumerable bodies, ranging below planet- 
oids and comets in their size, but yet occasionally of 
great magnitude, for some have been seen whose diam- 
eters were estimated at three-fourths of a mile. 

671. These bodies are not uniformly diffused through- 
out the solar system, but in some regions are scattered 
and sparse, while in others they are grouped together 
in vast multitudes, forming streams and rings of me- 
teors revolving in regular orbits about the sun. 

672. The November Stream. The star-showers of 
November proceed from a vast train of meteoric bodies, 
which revolves with a retrograde motion, around the 
sun in the period of 33^ years, its»orbit extending be- 
yond that of Neptune. The length of the densest por- 
tion of this train has been estimated at full 1,000,000,- 
000 miles, and its greatest thickness at 50,000 miles. 

673. The elements of a comet which appeared in 
1866 are almost identical with those of the November 
meteors, and it is therefore believed that this comet is 
one of the bodies belonging to this group. 

674. August Ring. The August group of meteors 
appears to form an unbroken ring, which revolves about 

What is the theory in regard to meteoric bodies ? What is said respecting their 
general size ? Are they uniformly distributed through space ? When are streams 
and rings formed? Describe the November stream ? The August zone? 



274 SOLAR SYSTEM. 

the sun with a retrograde motion. The periodic time has 
been computed at 121.5 years, and the thickness of the 
ring estimated at from five to eleven millions of miles. 

675. From the similarity of its elements, the third 
comet of 1862 has been regarded as belonging to the 
August group of meteors. 

676. Meteoric Phenomena. The various meteoric 
phenomena are supposed to arise as follows : — 

When the earth, in its annual progress, passes 
through the regions where these bodies are thinly dif- 
fused, they are attracted by the earth, and descend 
through the atmosphere with such velocity that they 
ignite, and are in most cases consumed. Under these 
circumstances, the ordinary phenomenon of shooting 
stars occurs. When the earth traverses the densely- 
crowded zones, star-showers are beheld ; and when any 
of the large solid masses enter the atmosphere of the 
earth, a meteorite with all its splendors sweeps across 
the sky, often attended by explosions which are fol- 
lowed by the fall of aerolites. 



CHAPTER VIII. 

TIDES. 



677. The periodical rising and falling' of the waters of 
the ocean in alternate succession are called tides. Standing 
on the sea shore, a person will perceive that for the space 
of nearly 6 hours the waters of the sea continue to rise 
higher and higher, overflowing the shores, and running 
into the channels of rivers. When they have attained 
their greatest elevation, it is then said to be high tide, 
full sea, or flood tide. Remaining at this elevation only 
for a few moments they then begin to fall, and continue 
to sink for about 6 hours more. When the waters have 
reached their greatest depression, it is then low, or ebb tide. 
After attaining this point, the sea in a short time again 

How are the various meteoric phenomena supposed to be caused ? What does 
Chapter VIII. treat of? What are the tides? Describe them, explaining the mean- 
ing of high tide and low tide ? 



TIDES. 275 

begins to swell in the same manner as before, and thus 
from year to year, and from century to century, the ebb and 
flow of the ocean follow each other at regular intervals 
of time. 

678. From the above explanation it will be seen that 
there are daily two high tides and two low tides The in- 
terval of time between two successive high or low tides, 
is about 12h. 25m. Accordingly when there is a high 
tide at any place, as New York, for instance, there must 
also be a high tide on the opposite side of the globe, and 
the same is true in respect to a low tide. These points 
are illustrated in Fig. 79, where O and O 1 represent 
the places where the high tides, and B and C, those where 
the low tides simultaneously occur on the globe. 

FIG. 79 




HIGH AND LOW TIDES 



679. A marked correspondence exists between the 
motion of the tides and the motion of the moon. If to-day 
at 10 A. M., it is high tide in a certain harbor, it will be 
high tide to morrow in the same harbor at 10h'. 50m. 
28sec. A. M. The interval therefore that elapses be- 
tween any high tide and the next but one after it, is 24h. 
50m. 28sec. Now this is the exact amount of time that 
intervenes between two successive passages of the moon 
over the meridian of any place. In fact as the earth re- 
volves on her axis, the tide wave tends to keep under the 
moon, and thus sweeps around the globe from any port 
to the same port again, in the precise period of time that 

How many high tides and low tides occur daily? What is the interval of time between 
two successive high or low tides? When a high tide for instance occurs at any port 
where is there then also another high tide ? Explain the Figure. What marked correa 
pondence is here alluded to 1 Describe it particular^ 1 



276 SOLAR SYSTEM. 

elapses between two successive returns of the moon to the 
meridian of this port. 

680. Cause of the Tides. The unequal attraction 
exerted by the sun and moon upon different parts of the globe 
-produces the tides, and we will now proceed to explain 
this phenomenon, commencing with the moon. In 
Fig. 79, let M represent the moon, E the solid portion of 
the earth, and CDOFB and CD'O^B the ocean. Now 
every particle of matter belonging to the globe is at- 
tracted by the moon, with a force which varies inversely 
with the square of the distance of the particle from the centre 
of the moon. l It is evident, that under the influence of 
this varying force, the solid portion of the globe will re- 
main imperceptibly unchanged in form, because the atoms 
that compose it, are bound together in a mass, and if one 
particle moves all the rest move with it. But the watery 
atoms move freely, and are influenced by the slightest va 
riation in the lunar attraction ; accordingly the moon 
tends to produce high tides directly beneath her as at 
and O 1 , and low tides half way between these points as 
at B and 0. 

681. Why high tides occur on opposite sides of 
the Globe. The waters of the globe, as represented 
in the figure, assume the form they possess under the 
action of two forces ; First, the force of gravitation by 
which they tend towards the earth's centre ; Secondly, 
the attractive force of the moon, by which they tend to 
move toward the moon's centre. Now on the side of 
the earth toward the moon, the waters about are 
drawn in one direction by the lunar, and in the opposite 
by the terrestrial attraction; but being nearer to the moon 
than the rest of the waters belonging to the hemisphere 
BOO they are consequently most attracted by this body, 
and by the influence of this excess of attraction are com- 
pelled to swell outwards towards the moon. Thus the 
waters in the vicinity of have their gravity towards the 
centre of the earth diminished by the disturbing action of 

1. See Art. 405. 

What is the cause of the tides ? Explain from Figure 79, the action of the moon in 
producing tides 1 Explain in full how high tides are product on opposite sides of the 
globe 1 



WHY LOW TIDES OCCUK, &C. 277 

the moon, and to restore their equilibrium, they here 
accumulate. 

682. The waters about O l , in the hemisphere BCMC 
are less attracted by the moon than on any other part of the 
ocean on the entire globe; because they are the most dis- 
tant from this luminary, and the attraction is here below 
its average value. Now asnhe moon's attraction at O 1 is 
directed towards the earth's centre sl deficiency of lunar at- 
traction at O l , necessarily diminishes the gravity of the 
waters about O. 1 They are consequently heaped up at 
this point, just as in the former case, and the elevated 
surface of the sea assumes an oval form. 

683. Why low tides occur on opposite sides of 
the Globe. At the places B and C, the action of the 
moon is oblique to the surface of the ocean, and it is evi- 
dent that if any particle of water at B, is drawn by the 
lunar force in the direction BM, it will not only ap- 
proach the centre of the moon but also the centre of the 
earth. 1 Now that part of the lunar force which produces 
this latter motion, acting upon the waters in the direction 
of terrestrial gravity, and in addition to it, necessarily 
depresses them more than usual ; they accordingly fall, 
in order to regain their equilibrium, and the surface of 
the ocean becomes flattened at B and at C. 

At then the excess of the direct action of the moon 
raises the waters of the sea, and at O 1 a deficiency of this 
direct action produces the same effect; while at 90° 
degrees distance from these points ; viz., at B and C her 
oblique action depresses them. 

684. As we advance from B or C towards 0, in the 
hemisphere BOC, the action of the moon becomes less and 
less oblique to the surface of the sea, and her power to 
depress it and increase the gravity of the waters gradually 
diminishes. At the distance of 35° from B and C, to wit, 
at F and D, this power vanishes, and upon passing thu 

1. That a force acting obliquely upon a body, tends to produce motion 
ji two directions is a well known fact. Take for instance the case of a boat 
sailing obliquely across a stream. Here the force of the wind carries the 
boat in two directions from its starting point at the same time ; viz., 
across the river and along the bank. 

Explain how two low tides are produced on opposite sides of the global 



278 SOLAR SYSTEM. 

limit the force of the moon tends to elevate the waters of 
the globe. 

685. In the opposite hemisphere BO l G a similar effect 
is produced. At the distance of 35° degrees from B 
and C; viz., at F 1 and D 1 , the moon ceases to increase 
the gravity of the waters, in the directions BE and CE, 
while those that occupy the remaining part of this hem- 
isphere; that is, F'OD 1 , are drawn towards the moon, but 
with varying force, according to their respective distan- 
ces from this body. Thus the waters at F 1 and D 1 will 
be drawn toward the moon and the solid part of the 
earth with more power than the waters atO 1 ; the latter, 
therefore, will virtually rise in respect to the former, 
and under this varying force the surface of the sea 
throughout the space FWD 1 will assume an oval shape. 

686. In fine, we may say, that the equilibrium of the 
waters of the ocean is disturbed by the action of the 
moon, and is not restored until they assume, under 
this action, the oval or ellipsoidal form in the manner 
described. 

687. Solar Influence. The sun like the moon pro- 
duces tides by the unequal attraction it exerts upon the 
waters of the ocean, causing high tides at the points im- 
mediately beneath it on opposite sides of the globe, as at 
and O 1 , and low tides at 90° distance from these 
points, as at B and C. The sun's influence is however 
only about one-third of that of the moon, notwithstand- 
ing its vast superiority in size and mass. But any dif- 
ficulty that may arise in understanding this fact will 
vanish, when we reflect that it is the unequal action of 
these bodies upon the waters of the earth that produces 
the tides, and not their whole attraction. Now the wa- 
ters at 0,Fig. 80, are about 8,000 miles (the earth's di- 
ameter) nearer the sun and moon than the waters at O 1 , 
but 8,000 miles is ^th part of the moon's distance from 
the earth while it is only y^o o tn P art °f tne sun ' s dis- 
tance 1 from the earth. 



1. The moon's distance from the earth is about 240.000 miles, which being 
divided by 8,000 miles, the quotient is 30. 8,000 miles is therefore ^Lth 

To what extent around B and O are the waters of the ocean depressed by the action of 
the moon, and to what extent elevated about O and O 1 1 What is said respecting the sun'» 
influence in producing tides * What '« «nid of the amoun' o f «o!ar influence 1 Bxplai* 
vhv it is small 1 



SPRING AND NEAP TIDES. 279 

We thus see that the attraction of the moon 
upon the waters of the opposite hemispheres is mani- 
festly unequal, while that of the sun is almost unchanged. 
The investigations of philosophers have proved that 
while, by the moon's influence, the waters of the ocean 
at and 0' are 58 inches higher than at B and C ; 
the difference caused by the action of the sun is only 
23 inches. 

689. Spring and Neap Tides. We have just seen 
that the sun and moon cause tides in the ocean, indepen- 
dently of each other. These bodies however are perpetu- 
ally changing their relative positions in the heavens, and 
on this account their separate actions are at alternate 
periods of time united and opposed to each other. The 
sun and moon act together twice a month; viz., at the 
syzygiesf and the tides are then unusually high, since the 
lunar and solar tide waves are then heaped one upon the 
other. These are the spring tides. 

690. Twice every month, at the quadratures, the sun 
and moon oppose each other ; for at those points on the 
earth's surface where the sun's action then tends to elevate 
the waters, the moon's influence depresses them, and where 
the moon raises the surface of the ocean, the influence of 
the sun is exerted to cause it to sink. These are the 
neap tides. 

691. The entire lunar ^&/ fluctuation being about 5 
feet and the solar 2, the average heights of the spring and 
neap tides will be in the ratio of 7 to 3. At the time of 
the neap tides, the low tides are higher than ordinary, since 
at the places where they occur the solar tide wave is at 
its greatest altitude and its height must be added to the 
height of the low water, caused by the moon's action. 
But the high tides are then unusually low, since the lunar 
high tide wave is diminished by the solar low tide. 

692. In Figs. 80 and 81, the subject of the spring tides 

part of the moon's distance from the earth. Calling the sun's distance from 
the earth in round numbers 96,000,000 miles, we find in the same way that 
8,000 miles is about Y2^oTr tn P art °f tne sun ' s distance from the earth. 

1. The tidal influence of the sun and moon is found according to the law 
of universal gravitation to be inversely as the cubes of their distances. 

2. See notes 1 and 2, page 148. 

What have philosophers showr respecting the heights of the solar and lunar tides t 
When do the spring tides occur 1 When the neap tides 1 



280 



SOLAR SYSTEM. 
FIG. 80. 




SPRING TIDE NEW MOON. 



is illustrated. In each of these figures, S represents the 
sun, M the moon, and E the solid portion of the earth. 
The dotted line inclosing the earth is the solar tide-wave, 



FIG. 81. 




SPRING TIDE FULL MOON. 



and upon this in the line of the three bodies, is heaped 
the lunar tide-wave, the boundary of which is the outer 
curved line. 

693. In Fig. 82, is exhibited the phenomenon of the 
neap tides. The moon is in quadrature, 90° from the sun, 
and the two bodies evidently counteract each other's 
influence in producing their respective tides. The solar 
tide wave, as in the preceding figure is represented by 
the dotted oval line, and the lunar tide wave by the un- 
broken curved line. 

694. Since a difficulty is sometimes experienced in 
understanding how a spring tide is produced when the 
sun and moon are on opposite sides of the globe, we will 
explain this point a little more particularly. In Fig. 
80, where the sun and moon are on the same side of the 
earth, it is the time of new moon, and a spring tide 

Descrile these phenomena in full, and explain from Figures 80. 81, and 82? 



TIME OF THE TIDE. 



281 



occurs. From the reasoning employed in Arts. 681-2, it 
will be perceived that the waters at are heaped up by 



FIG. 82 





NEAP TIDE QUADRATURE. 



the excess of attraction exerted by the sun and moon, to 
draw the waters from the centre of the earth, thus ren- 
dering them more convex than usual. Around O l 
there is a deficiency of solar and lunar attraction, and the 
waters in this region are drawn down less than usual 
toward the centre of the earth, and they are conse- 
quently higher than common. 

695. In Fig. 81, the sun and moon are on opposite sides 
of the earth. The moon is at her full, and a spring tide 
now also occurs. At the sun produces a high tide by 
his excess of attraction and the moon here causes a high 
tide by her deficiency of attraction, since that which is the 
nearest hemisphere to the sun is the farthest from the 
moon. At O 1 the moon's excess of attraction gives rise to 
the lunar high tide, while the sun's deficiency of attrac-- 
tion causes here likewise a solar high tide; for in this case 
the hemisphere which is nearest to the moon is the most 
i emote from the sun. 

696. Time of the tide. In Art. 679, we have said 
that there exists a marked correspondence between the 
motions of the tide, and those of the moon. If the waters 
moved with perfect freedom, the lunar tide wave would 

Show why a spring tide occurs at full moon ? 



282 SOLAR SYSTEM. 

be highest at any place when the moon was upon the merid- 
ian of the place '; and the solar tide wave highest when the 
sun was upon its meridian. But the waters do not at once 
obey the action of the sun and moon, on account of their 
inertia; and they are also retarded in their motion by 
the friction produced in their passage over the bed of the 
sea and the sides and bottoms of channels. It thus hap- 
pens that the high tide does not occur at any place until 
the moon has passed its meridian several hours. 1 The 
interval between high tide and the moon's meridian 
passage is however not constant, but varies in different 
places. 

697. Priming or Lagging of the Tide. The actual 
high tide at any part is produced by the union or super- 
position of the solar and lunar tide waves. Now on ac- 
count of the changing relative positions of the sun and 
moon, these waves do not so unite as to make the high 
tides recur at any port at the expiration of exactly equal 
intervals of time. The tide days therefore, are not of the 
uniform length of 24h. 50m. 28sec, but vary somewhat in 
duration, and this variation is quite marked about the 
time of the new and full moon. 

698. Effect of Declination on the height of the 
Tide. The highest point of the tide wave, tends to 
place itself directly beneath the body which raises it, so 
as to be exactly in the line joining the centres of this 
body and of the earth. If therefore the sun and moon 
were always found in the plane of the equator, the 
tides would be highest in the equatorial regions, while a 
constant low tide would exist at the poles. But these lu- 
minaries are not thus situated, since, owing to the obli- 
quity of the ecliptic, they have an apparent motion north 
and south of the equator ; the sun departing from the 

1. At Dunkirk, for instance, high water occurs half a day after me 
moon passes its meridian, at St. Malo's six hours, and at the Cape of Good 
Hope, one and a half hours. 

Why does not the high tide occur at any place when the moon is exactly on its merid- 
ian ? How long a period sometimes elapses after the moon has passed the meridian before 
the high tide happens ? Is the interval between the time of high tide at any place, and the 
moon's meridian passage, invariably the same 7 Explain what is meant by the priming 
and lagging of the tide? Are the tide days of uniform length? When is the variation 
greatest? Why do tt« declinations of the sun and moon influence the tides? 



ACTUAL HEIGHTS OF THE TIDE. 283 

equator about 23 \ degrees, while the moon attains a 
declination of 29° on one side, and about 17° on the 
other. 

699. These changes in the position of the sun or moon 
accordingly affect the height of the tide at any particu- 
lar place. When the moon, for example, has her great- 
est northern declination, the daily high tides will be 
highest in all those places in the northern hemisphere where 
the moon is above the horizon, and lowest where she is 
below the horizon. In the southern hemisphere the phe- 
nomena are reversed ; the daily high tides being highest at 
all those places where the moon is beneath the horizon, 
and lowest in all the regions where she is above the hori- 
zon. A glance at Fig. 83, proves these statements. 

FIG. 83. 




700. Actual heights of the Tide. The theoretical 
height of the tide does not correspond to the real height. 
This difference is owing to local causes, such as the union 
of two tides or the rushing of the tide wave into a nar- 
row channel. In the latter case the advance of the tide 
is often very rapid, and the water rises to a great eleva- 
tion. Thus within the British Channel, the sea is so 
compressed that the tide rises 50 feet at St. Malo's, on the 
coast of France. In the Bay of Fundy, the tide swells 
to the height of 60 or 70 feet. Here, according to Prof. 

State why these changes in the position of the sun or moon affect the height of the tide 
at any particular place 1 Why does not the theoretical height of the tide at anyplace 
correspond with the actual height ? 



284 SOLAR SYSTEM. 

"Whewell, the tide-wave of the South Atlantic, meets the 
tide-wave of the Northern Ocean, and their union raises 
the surface of the sea to the height just mentioned. On 
the vast Pacific, where the great tide-wave moves with- 
out obstruction, the rise of the water is only about two 
feet on the shores of some of the South Sea Islands. 

701. Derivative 'Tides. The tides perceptible in 
rivers, and in seas communicating with the ocean, are 
termed derivative tides, as they are but portions of the 
great oceanic tide waves. The derivative tides ascend 
the large rivers of the globe to a great distance from their 
mouths; but their progress is so much retarded by their 
friction against the banks and by various impediments, 
that several tides in some instances are found at the same 
time along the same river. Thus, in the Amazon, five 
hundred miles from its mouth, the tide is distinctly per- 
ceptible ; and so much is it retarded in ascending this 
stream, that during the equinoxes, for three successive 
days, five tide-waves, rising from 12 to 15 feet, follow 
each other daily up the river. 

702. Nature and Velocity of the Tide- Wave. The 
tide-wave is a vast undulation of the ocean which af- 
fects it from the surface to the bottom. It originates 
in the Pacific, off the coast of South America, and if 
unobstructed, would move westward at the rate of about 
1,000 miles an hour ; but the shallow parts of the ocean 
lessen this speed, and the undulation advances with a 
velocity dependent upon the depth of the sea which it 
traverses. Thus at the depth of 60 feet the velocity 
of the wave is 25 miles. an hour, at 600 hundred feet 80 
miles an hour, and at 24,000 feet, 500 miles an hour. 

703. Cotidal Lines. Checked by islands and op- 
posing continents, and retarded by the causes already 
mentioned, the problem of the tides becomes extremely 
complex, and their phenomena are principally ascer- 
tained by observation. The results thus obtained are 

State the cases cited ? Explain derivative tides ? State what is said respecting de- 
rivative tides ascending long rivers ? Give the facts in regard to the Amazon ? Whs t 
is the nature of the tide-wave ? Where does the tide originate ? What would be i ts 
velocity if it was unchecked ? Why is the speed retarded ? Upon what does the speed 
depend ? Give examples ? Why is the problem of the tides extremely complex ? 
How are its phenomena principally obtained ? 



TERRESTEUL LONGITUDE. 285 

delineated on maps by drawing lines through the places 
where high water occurs at the same moment of abso- 
lute time at new and full moon. These lines are 
termed cotidal lines. 

704. Tides in Lakes and Seas connected with the 
Ocean. The attractive force exerted by the moon upon 
the waters of a lake is so nearly the same in every part 
of it that the sensible difference of force is very small, 
and the tide due to this difference is consequently very 
slight ; still less will be the solar tide ; it is only, there- 
fore, in large lakes that a tide can be detected. From 
observations, made at Chicago, in 1859, it appears that 
Lake Michigan has an average tide of If inches. 

705. In the Mediterranean Sea, which is almost sur- 
rounded by land, the mean height of the tide is about 18 
inches. In the Black Sea the tide is scarce perceptible. 

706. The atmosphere, like the ocean, has its tides, but 
it is barely possible to detect them. 



CHAPTER IX. 

TERRESTRIAL LONGITUDE. 

r 

707. In order to determine the precise situation of a 
place on land, or a ship at sea, their respective latitudes 
and longitudes must be known, (Art. 58.) It is of the 
utmost importance to mankind that these measure- 
ments should be ascertained with great accuracy, espe- 
cially on the ocean, in order that the mariner may know 
his exact position in the midst of dangers, that threaten 
the lives and property entrusted to his care. 

708. Latitude has already been explained and one 
method given by which it can be obtained, (Art. 57 ;) 
we shall now speak of longitude and briefly unfold the 
several methods by which it is determined. This prob- 

How are the results obtained represented ? What are cotidal lines ? V. hat is said 
respecting the tides of lakes ? Are tides perceptible in large lakes ? What is stated 
respecting the tide of Lake Michigan ? What of those of the Mediterranean and 
Black Seas? Has the atmosphere tides ? What is the subject of Chapter VIJT. ? How 
is the exact position of any place on land or sea ascertained ? Why is it important to 
mankind that these measurements should be precisely determined ? 



286 SOLAR SYSTEM. 

* 

lem is intimately connected with astronomy; inasmuch 
as eclipses and the motions of the moon afford methods 
most highly prized and extensively employed for ascer- 
taining the longitude. On this account the subject of 
longitude was not introduced in connection with lati- 
tude, but was deferred until the lunar motions and the 
phenomena of eclipses in general had been discussed. 

709. Longitude. The longitude of any place is its dis- 
tance east or west of a given meridian, measured in degrees, 
minutes, and seconds. It can be ascertained hjfour meth- 
ods ; 1st. By chronometers 1 ; 2nd. By means of eclipses ; 
3d. By the electric telegraph ; 4th. By the lunar method. 

710. By Chronometers. Supposing, for example, 
that it is now 12 o'clock at Greenwich, the sun being 
there on the meridian, it is evident that at any place 
15° east of Greenwich, it must at this instant be 1 
o'clock ; (Art. 104,) because this place, owing to the rota- 
tion of the earth, was in the same position in respect to 
the sun an hour ago, as Green wich now is. Moreover, 
at a place 15° west of Greenwich it is now 11 o'clock, 
because the sun will not be on the meridian of this place 
until an hour after it is noon at Greenwich. The heal 
time of the first station will accordingly be faster than 
Greenwich time by one hour, and that of the second 
slower by the same quantity. 

711. JSTow if a person were to travel around the globe 
from east to west or from west to east, with a chronometer 
that kept true Greenwich time ; he could readily ascer- 
tain the longitudes of each of the several places where he 
arrived, reckoning from the meridian of Greenwich, by 
finding the difference between their respective local times 
and the Greenwich time, as indicated by his chronometer 
Thus, if he traveled west to Toronto, the difference be 
tween Toronto and Greenwich time, would be 5h. 17m 
26sec, which corresponds to 79° 21 / 30", and. is the Ion 
gitude of Toronto west from Greenwich. The diffei 

1. A chronometer is a time-keeper, constructed like a watch, made witl 
great care and skill in order that it may measure time as perfectly as possible 

W*v is the problem of longitude connected with astronomy 7 Define longitude ? State 
the/ <r methods by which it can be determined'? Explain what is meant by local time? 
Rho how longitude can be determined by the chronometer ? Oive the example t 



BY ECLIPSES. 287 

mces 1 between the local times of two or more places thus 
measure the differences of their longitudes. 

712. If chronometers kept perfect time, no other method 
would be required to determine the longitude, but they 
are liable to errors in their rate of going, and though 
they have of late been greatly improved, yet they can 
not in general be relied upon for this purpose. 8 . 

713. By Eclipses. The eclipses of Jupiter's satellites 
are phenomena, which are visible at once from all parts 
of the world where the planet is above the horizon. It 
therefore to-night an eclipse of a satellite should be 
noted at any two places on the globe, the difference in 
the local times of these places would give the difference of 
their longitudes. 

714. But the laws that govern the motions of these 
bodies are well known, and the time of the occurrence 
of their eclipses at any station, as at Greenwich Obser- 
vatory, can be calculated beforehand. Such calculations 
are accordingly made and published in tables. 

When, therefore, an observer at New York, for in- 
stance, notes a certain eclipse of a satellite, he can as- 
certain the longitude of his station by taking his Green- 
wich tables, finding the time when this eclipse was 
predicted to occur at that observatory, and then com- 
paring it with the local time of New York when the same 
event happened there. 

715. The eclipses of the sun and moon are employed 
for the same purpose. This mode of obtaining the lon- 
gitude does not admit of great accuracy, since it is im- 

1. A difference in local time of one hour corresponds to 15° of longitude, 

" " " of one minute " " 15' " " 

" " " of one second " " 15" " " 

2. Chronometers have however been constructed of surpassing accuracy. 
Thirty years ago an English artist of the name of French made two chro- 
nometers, which kept time with such exactness, that with one of them a 
navigator could have sailed to China and back again without making 
more than half a mile of error in his longitude. And with the other he 
could have sailed around the world, without having his greatest error in 
longitude exceed fifty or sixty rods. 

Of what are the differences of local times the measures? Why can not chronometer* 
in general be relied on for determining the lovgittide? Explain how longitude can be as- 
certained by means of eclipses ? What other eclipses Besides those of Jupiter's satellite* 
are employed for this purpose 3 

13 



288 SOLAR SYSTEM. 

possible to determine with perfect precision the exact 
moment when an eclipse begins and ends. ' It is of no use 
to the mariner, for it can only be employed on land. 

716. By the Electric Telegraph. If two places 
are connected by telegraphic lines, the difference of their 
longitudes can be easily obtained by transmitting signals 
from one station to the other, and finding the difference in 
their local times. Thus, for example, if at the very 
moment a star is on the meridian of Philadelphia an ob 
server there touches the telegraphic key and signalizes 
the fact to "Washington, the touching of the key at the for- 
mer city, and the movement of the recording pen at the latter 
occur simultaneously. Then, by comparing the Phila- 
delphia time when these events happened with the 
Washington time, the difference in the local times of the two 
cities is obtained, and consequently the difference in 
their longitudes. 2 

717. In this manner, substantially, the respective dif- 
ferences of longitudes between Washington, Philadel- 
phia, and Jersey City, were ascertained with great 
exactness in the summer of 1847. 

In the following year, the difference of longitude be- 
tween New York and Cambridge, and also that between 
Philadelphia and Cincinnati, were obtained by the snme 
method. 

718. This mode of determining longitude is not of 
universal application, but is regarded as one of the best 
wherever it can be employed, since it admits of great 
accuracy. 

719. Lunar Method. The motions of the moon are 



1. In the determination of the longitude by means of an eclipse it must 
necessarily be observed by different persons, and with different telescopes. 
But telescopes vary in their power of revealing objects, and observers differ 
in the keenness of their vision. It thus happens that two persons, side bj 
side, may assign different times to the beginning or ending of an eclipse. 

2. Since the electric current occupies about one second of time in going 
through a space of 16,000 miles, allowance must be made for this retar- 
dation in very long distances. In short distances it may be safely neg- 
lected. 



Why is not this mode of determining the longitude one of great exactness"? Where 
can this mode only be used ? Explain in what manner the longitude is obtained by 
the electric telegraph 1 In what instances has it thus been determined 1 What is said re 
specting the extent to which this mode can be employed ? What in regard to the accu 
racy attainable bv it 1 



LUNAR METHOD. 289 

now so well known, and her course through the heavens 
so precisely ascertained, that an astronomer can predict 
for every tenth second of time, for years to come, the places 
of the moon in the sky corresponding to these seconds. 
Her exact position being fixed, by ascertaining her dis* 
tance from the sun, and from certain of the planets and 
several conspicuous stars that lie along her pathway in 
the heavens. 

720. Tables of the moon's positions are computed with 
great care at well known observatories, in the reckon- 
ing of their respective local times ; and by the aid of 
these, an observer, either on sea or land, determines the 
longitude of his station without difficulty. 

721. The problem is thus solved. If a sailor, for in- 
stance, observes at 10 o'clock P. M., according to his own 
time, the position of the moon in respect to Jupiter, and 
finds upon turning to his Greenwich tables, that she is 
in the same position at Greenwich at 8 o'clock P. M. ; he 
knows at once that he is in longitude 30° east of Green- 
wich ; for the difference in the local times is two hours^ 
and the Greenwich time is behind his own. 

Describe the lunar method, and give the illustration 1 



290 THE STAERY HEAVENS. 



PART THIRD. 

THE STARRY HEAVENS, 



CHAPTER I. 



OF THE FIXED STARS IN GENERAL AND THE CONSTELLATIONS. 

722. We pass now in imagination beyond the solar 
system and direct our attention to those heavenly bodies 
that lie beyond it. 

723. The Fixed Stars. When we gaze at night 
upon the unclouded sky we behold, in addition to the 
objects already described, a multitude of sparkling orbs, 
varying in brightness and magnitude. These are termed 
the fixed stars, not because they are known to be actu- 
ally stationary in space, for many of the stars are un- 
doubtedly in motion, and possibly all may be ; but from 
the fact that their changes in position, wherever noticed, 
are so slow, that compared with the swiftly moving mem- 
bers of the solar system, they may be regarded as fixed. 

724. Magnitudes. Astronomers have classed the 
fixed stars according to their degrees of brightness. Those 
possessing the greatest splendor are termed stars of the 
first magnitude, while others which differ from the first 
by a perceptible diminution of brightness rank as stars of 
the second magnitude ; and so on to the seventh magnitude, 
which is the limit of visibility to the naked eye. But the 
telescope now comes to our aid, and we discern stars rang- 
ing down in minuteness from the seventh to the sixteenth 
magnitude ; and even beyond, the series ending, not from 
the want of stars to discover, but because our nobtest 
instruments have not sufficient power to detect them. 

725. It will be readily seen that this mode of classifi- 

What does Part Third treat of? What is the subject of Chapter 1. 1 To what do we 
now direct our attention 1 What is said of the fixed stars ? How have they been classed 
by astronomers ? How many magnitudes are visible to the naked eye ? How far are thesa 
magnitudes extended by the teUwone 1 



NUMBER OF STARS. 291 

cation is arbitrary in its nature. The diminution in 
brightness, which distinguishes a star of one magnitude 
from that which immediately precedes it, can not be de- 
termined with mathematical precision, and is estimated 
by the eye alone. It therefore will vary with different 
persons, and it is impossible to tell where one magnitude 
ends and another begins ; nevertheless, usage has deter- 
mined among astronomers under what magnitudes are to 
be placed the numerous stars mapped down upon their 
star-charts and celestal globes. 

726. It must also be borne in mind, that the assumed 
magnitude of a star determines nothing as to its real size. 
Fo, r the fixed stars are at different distances from us, and 
consequently a star of moderate size may, from ics com- 
parative proximity, shine with great splendor and be a 
conspicuous object in the heavens — while anotfter, which 
far surpasses it in intrinsic brightness and magnitude, 
may yet be so remote as to rank many degrees of mag 
nitud* 3 below the former, and perhaps be merged in ob 
scurity amid crowds of orbs possessing equal splendor 

727. Number of Stars. The stars are literally in 
numerable. There are but 23 or 24 of the first magni 
tude, from 50 to 60 of the second, about 200 of the third 
and as we descend in the scale the number comprised in 
the different classes rapidly increases. The number 
already noted down, from the first to the seventh magni- 
tude inclusive, amounts to from 12 to 15,000, while the 
entire number registered amounts to 150,000 or 200,000. 

728. But when the telescope sounds the depths of 
space, the heavens appear to be blazing with bright 
orbs, and the more powerful the instrument the more 
numerous are the stars revealed. Sir Win. Herschel 
estimated, that, in a certain region of the sky remarkably 
rich with stars no less than 116,000 passed through the 
field of his telescope in the space of fifteen minutes, and 

Do the magnitudes mentioned include all the stars that exist T What is said respecting 
this classification 1 Does the assumed magnitude of any star determine any thing respect- 
ing its actual size ? Why not 1 What is said respecting the number of the stars ? How 
many are thereof the first magnitude? Of the second ? Of the third ? What is said 
of their number as we descend in the scale 1 How many are noted down from the first to 
the seventh magnitude ? What is the amount of the entire list registered ? What is said 
of the number of stars observed when the telescope is employed ? What estimate wai 
made by Sir Win Herschel 7 



292 STARRY HEAVENS. 

throughout the entire expanse of the heavens, it is reck- 
oned that at least one hundred millions of stars are within 
the range of telescopic vision. 

729. Distance of the Fixed Stars. We have seen 
(Page 65, note) that the parallax of a heavenly body 
(as the moon) can be obtained, when it is viewed by 
different observers at the same time from different parts 
of the earth. And the parallax being known, the dis- 
tance of the body from the earth can be computed without 
difficulty, (Art. 263.) 

730. But when we attempt the same mode of obser- 
vation on a fixed star, no parallax can be obtained; for so 
distant is the star, that the supposed lines drawn to it 
from the different places of observation make no appre- 
ciable angle with each other, but are parallel. 

731. Astronomers, have therefore adopted another 
method, which consists in observing the position of a star 
in the heavens at some particular time, and repeating the 
observation six months afterwards, when the earth is in 
the opposite part of her orbit. The astronomer thus 
notes the situation of the star from two stations in space 
190,000,000 miles asunder. But even this vast interval 
between the two points of observation produces so small 
a displacement of the star in the heavens, that obser- 
vers were unable, until lately, to determine whether the 
star was really unchanged in position or not. 

732. Accordingly if an inhabitant of one of the new. 
est fixed stars (if such inhabitants there are) were able to 
discern the earth, it would be difficult also for him to 
decide whether it moved or not in the heavens ; for the en- 
tire space comprised in its orbit would at this immense dis- 
tance occupy but a mere point of the sky. 

733. In the beginning of the present century astron- 
omers had advanced so far in their knowledge of the 
fixed stars, as to feel confident that no star visible in the 
northern latitudes could have a greater parallax than 1", 

How many stars are believed to be w'.thin the range of telescopic vision ? How is the 
distance of a i*avenly body obtained 1 Can the perallax of a fixed star be found in the 
same way as that of the moon 1 What other method has been pursued by astronomers 1 
Has it succeeded 1 Would the earth in passing from one part of its orbit to the opposite^ 
change its apparent place in the heavens if observed from the nearest fixed star 1 What 
knowedge ha I astronomers of the parallax of the fixed stars at the beginning of the pres- 
ent century 1 



PARALLAX AND DISTANCE OF ALPHA CENTAURI. 293 

when, viewed from two points in space separated by an 
interval equal to the distance of the earth from the sun. 
They had not succeeded in determining the exact value 
of the parallax of any star, yet they were sure that it 
could not exceed the quantity just mentioned. But since 
the above period the problem has been solved. The 
able astronomers of Europe, changing their method of 
investigation, at last directed their exquisitely con- 
structed instruments towards a class of stars, termed 
binary stars (of which we shall soon speak,) and from 
numerous series of observations of the most refined na- 
ture have at length determined the parallax of several fixed 
stars. 

734. Parallax and Distance of Alpha Centauri. 
In the years 1832 and 1833, Prof. Henderson, of Edin- 
burg, made an extended series of observations, at the Cape 
of (rood Hope, upon the star Alpha in the constellation 
of the Centaur, (a Centauri) one of the brightest stars 
of the southern hemisphere, from which he deduced a 
parallax of V. Other observations, made by Mr. Mac- 
lear in 1839 and 1840, with a much finer instrument 
gave almost precisely the same result. 

735. # The parallax of Alpha Centauri, exceeds the 
known parallax of any other star, and, since the greater 
the parallax the less the distance, (Art. 95,) we may re- 
gard this star as the nearest of all the fixed stars. Since 
we know its parallax, we can compute its distance from 
the earth in miles, by proceeding in the manner we have 
frequently explained before. 

736. In Fig. 84, let S represent the star a Centauri, 
AB the radius of the earth's orbit, S A and SB two imagi- 
nary lines drawn from the star, one to the sun at B, and 
the other to the earth at A ; ASB an angle of \" and 
BAS a right angle. Now take A'B^ 1 a triangle similar 
to ABS, and supposing S l A l to be one mile in length 
A'B 1 will he, forty-eight thousand four hundred and eighty- 
one ten thousand millionths of a mile (.0000048481 miles.) 

Since this period has the parallax of any star been discovered? In what manner? 
Give an account of the researches of Prof. Henderson and Mr. Maclear ? What is the 
parallax of Alpha Centauri? How does it compare in amount with that of other fixed 
stare ? What inference is made from this fact? Having the parallax of a star, explain 
how its distance from the earth can be computed ? 



294 STARRY HEAVENS. 

737. Calling AB 95,000,000 miles, we obtain from 
the similar triangles the following proportions; viz., 
AJB 1 (.0000048481ths miles) : S'A 1 (1 mile) : : AB 

FIG 84. 




DISTANCE OF A FIXED STAR. 

(95,000,000 miles) : SA : multiplying the second and 
third terms together and dividing by the first, we obtain 
the value of SA, the distance of the earth from the star, l 
and .find it to be nearly 19,600,000,000,000 miles, almost 
twenty millions of millions of miles. 

737. The velocity of light is i 92, 000 miles per second, 
it would therefore take a ray of light about three years 
and a quarter to travel from the nearest fixed star to the 
earth. 

738. Parallax and Distance of 61 Cygni. In 
1838, Bessel, the renowned astronomer of Konigsberg, 
ascertained, beyond a doubt, the parallax of a double 
star in the constellation of the Swan, termed 61 Cygni. 
It was found to be about one third of a second (.348") 
which proved that this star was distant from the earth, 
592,000 times the earth's distance from the sun. It would 
take a ray of light more than nine years to pass from this 
star to our globe. Up to the present time the parallax 
of nine stars has been obtained, with more oi less 
exactness. 

739. Nature and Intrinsic splendor of the 
Fj xed Stars. The fixed stars are supposed to be suns 

1. The distance of the star from the earth may be regarded as equal to 
Its distance from the sun for the reason mentioned in (Art. 732.) In the 
above figure therefore the line SB may be considered equal to SA. 

What is the distance of the star Alpha Centauri from the earth in miles ? How mar* 
years would it take for a ray of light to travel from this, the nearest fixed star, to the earth ? 
When and by whom was the parallax of 61 Cygni discovered ? How great is it? How 
fat is this star from us 1 Of how many stars has the parallax been computed 1 



the constellation; HEIR USE. 295 

shining by their own light, and the analysis of the 
prism strengthens this view, as their spectra have been 
found, by Huggins, Secchi, and others, to be crossed 
by dark lines, like the spectrum of the sun. 

Thus the spectrum of Aldebaran reveals dark lines 
which indicate in this star the presence of sodium, 
magnesium, hydrogen, calcium, iron, bismuth, tellurium, 
antimony, and mercury. 

In the same manner Alpha Orionis is shown to pos- 
sess sodium, magnesium, calcium, iron, and bismuth ; 
Beta Pegasis, sodium, magnesium, and perhaps, bari- 
um ; Sirius, sodium, magnesium, hydrogen, and prob- 
ably iron, while Alpha Lyrae presents the same ele- 
ments as Sirius. 

Some of the fixed stars greatly exceed our sun in 
splendor, since from computations based upon parallax, 
it has been estimated that Alpha Centauri has an in- 
trinsic brilliancy nearly four times greater than that 
of the sun, while Sirius shines with the brightness ex- 
ceeding that of sixty suns. 

THE CONSTELLATIONS. 

740. For the purpose of distinguishing the fixed 
stars from one another, they have been divided, from 
the earliest ages 1 , into groups termed constellations, 
whose outlines are supposed to represent the figures 
of men, and also of animals and other objects, whose 
names they respectively bear ; but only in a few cases 
is there any approximate resemblance. 

741. The Stars in the Constellations. — How 
designated. The brightest stars of each constellation 

1 . In the book of Job, which, according to chronologists, was written 
at least 3,300 years ago, the constellations of Orion and the Pleiades 
are particularly men tion ed . The oldest Greek poets also speak of several 
of the constellations and principal stars. Thus Homer mentions Orion, 
the Bear, the Pleiades, and Hyades. 

What is said of the nature of the stars ? How is this view strengthened ? What 
elementary bodies have been found in Aldebaran, Alpha, Orionis, Beta Pegasi, Sirius, 
and Alpha Lyrae ? What is said of the splendor of Alpha Centauri and Sirius ? 
How have the fixed stars been grouped from the earliest ages ? Is there any re- 
semblance between the outlines of the constellations and the objects they are named 
after? 



296 SOLAR SYSTEM. 

are designated, in the order of their brilliancy, by 
the letters of the Greek alphabet. For example « Lyrse , 
or Alpha Lyrae, is the brightest star in the constellation 
of the Lyre, § Orionis, or Beta Orionis, the second 
brightest star in the constellation of Orion, and so on. 
"When the Greek letters are exhausted, the Roman 
alphabet and then numerals are employed. When a 
capital letter follows a number, the catalogue of some 
astronomer is referred to. Thus, 64 H. indicates the 
64th star in a certain constellation in Herschel's cata- 
logue. Some of the more brilliant stars have received 
proper names, as Sirius, Aldebaran, Arcturus, Regu- 
lus, and so forth. 

743. Conspicuous Constellations described. The 
Great Bear is a noted constellation in the northern 
heavens. It contains seven bright stars which present 
the outline of a dipper, four constituting the bowl, and 
three the handle in the tail of the Bear. The two 
stars in the bowl, on the western side, are called the 
pointers, because they are almost in a straight line 
with the pole star. 

The Lesser Bear also contains seven small stars, 
arranged somewhat in the shape of a dipper. The 
star at the end of the handle is the pole-star. 

Cassiopeia is known by the outline of a chair, formed 
by six stars, four of which constitute the legs, and two 
the back. This constellation is on the side of the pole 
opposite the tail of the Great Bear. 

The Swan, situated in the Milky Way, and south- 
west of Cassiopeia, is conspicuous for five bright stars 
in the shape of a cross, three in the Milky Way form- 
ing the body and neck, and the others the wings. 
Arided in the body is a star of the first magnitude. 

The Lyre, west of the Swan, is noted for a brilliant 
white star of the first magnitude. 

744. South of Cassiopeia is the constellation of An- 
dromeda, characterized by three stars of the second 

Explain the manner in which the stars of a constellation are rated in respect to 
brightness ? Have proper names been given to stars ? 



CONSTELLATIONS. 297 

magnitude and two of the third. Southwest of An- 
dromeda is Pegasus. Three of its brightest stars, 
with Alpheratz in Andromeda, form the noted square 
of Pegasus. Bootes is known by Arcturus, a beauti- 
ful reddish star of the first magnitude. 

745. Taurus , or the Bull, is remarkable for two con- 
spicuous clusters of stars, viz : The Pleiades and 
Hyades. The Pleiades are in the shoulder of the Bull. 
To the naked eye this group appears to consist of six 
or seven stars, but more than 200 have been revealed 
by the telescope. The Hyades, in the head, south- 
east of the Pleiades, are recognized by several stars 
in the shape of the letter V. Forming the eastern end 
of the letter is Aldebaran, a red star of the first mag- 
nitude. 

746. The constellation of Orion is one of exceeding 
splendor. It is remarkable for four brilliant stars ar- 
ranged somewhat in the form of a parallelogram, in- 
tersected at the middle by three conspicuous stars 
called the Belt of Orion, or the Ell and Yard. In the 
book of Job they are termed the bands of Orion. These 
three stars point in one direction to the Hyades and 
Pleiades, and in the other to Sirius. In this constel- 
lation 70 stars are visible to the naked eye. South- 
east of Orion is the constellation of Canis Major, chiefly 
distinguished for containing Sirius, or the dog star, 
the most magnificent of all the fixed stars. 

747. East of Taurus is the constellation of the 
Twins, which is known by two bright stars, Castor 
and Pollux, the former of the first magnitude, the lat- 
ter of the second. The Lion is a very large constel- 
lation. It is conspicuous for a semicircle of six bright 
stars which form with Regulus, a star of the first mag- 
nitude, the outline of a sickle, Regulus being at the 
end of the handle. 

748. Principal Constellations. A list of the chief 
constellations is given below. 

Describe the constellations which are niost conspicuous ? 



298 STARRY HEAVENS. 



CONSTELLATIONS NORTH OF THE ZODIAC. 

Cassiopeia, Lyra, the Harp, Bootes, 

Andromeda, Aquila, the Eagle, The Northern Crown, 

The Triangles, Antinous, Ursa Minor, the Lesser 

Perseus, Sobieski's Shield, Bear, 

The Camelopard, Sagitta, the Arrow, The Fox and Goose, 

Auriga, the Charioteer, Ursa Major, the Great Cygnus, the Swan, 

The Lynx, Bear, Delphinus, the Dolphin, 

The Lesser Lion, The Dragon, The Lesser Horse, 

Hercules, Berenice's Hair, Pegasus, the Winged Horse, 

TnE Serpent, The Greyhounds, Cepheus. 
Ophiuchus, 

CONSTELLATIONS OF THE ZODIAC. 

Aries, the Ram, Leo, the Lion, Sagittarius, the Archer, 

Taurus, the Bull, Virgo, the Virgin, Capricornus, the Goat, 

Gemini, the Twins, Libra, the Scales, Aquarius, the Waterbearer, 

Cancer, the Crab, Scorpio, the Scorpion, Pisces, the Fish. 

CONSTELLATIONS SOUTH OF THE ZODIAC. 
Cetus, the Whale, The Great Dog, Coryus, the Crow, 

Eridanus, The Lesser Dog, Centaurus, the Centaur, 

Orion, Argo Navis, the Ship, Lupus, the Wolf, 

The Hare, The Hydra, The Southern Fish. 

The Unicorn, The Cup, 

749. The Celestial Globe. A celestial globe is a 
sphere, on the outer surface of which the constellations 
are delineated, and numerous stars and other objects 
in the visible heavens laid down with as much precision 
as possible. 

It is, therefore, & faithful copy of the celestial sphere. 
Ninety degrees from each pole a strongly marked line 
encompasses the globe representing the celestial equa- 
tor, and inclined to this, at the angle indicating the 
obliquity of the ecliptic (23° 27' 43".4) is another great 
circle, representing the ecliptic. One of the points 
where these two great circles intersect is the first of 
Aries. From this point the celestial equator is grad- 
uated into degrees and parts of degrees, indicating arcs 
of right ascension ; and from the same point the ecliptic 
is graduated in like manner into arcs of celestial longi- 
tude. The ecliptic is, moreover, divided into the twelve 
signs, marked with their corresponding months and 
days. 

750. The globe is surrounded by a brass ring, the north 
and south poles of the former being connected with the 

Recite the names of the principal constellations north of the Zodiac ? Recite the 
names of the principal constellations of the Zodiac, and of those south of the 
Zodiac ? Describe the celestial globe ? 



HOW TO USE THE GLOBE. 299 

latter by means of pivots; so that the glooe can easily 
revolve within the ring. The brass ring is accordingly 
a celestial meridian, and being graduated from the 
equator to either pole, from 0° to 90°, it measures arcs of 
declination. This ring, with the globe attached to it, is set 
upright in a socket in which it readily slides, so that any 
required elevation can be given to the poles of the globe. 
Enclosing the whole, and mounted upon a frame, is a 
flat, broad ring representing the celestial horizon ; on the 
surface of which, for the sake of reference, the signs of th? 
zodiac are drawn, and the sun's place in the ecliptic set 
down for every day in the year. 

751. Around one of the poles of the globe a small 
circle is described having the pole for its center, the 
circumference being divided into 24 equal parts, marking 
the hours of the entire day. Attached to the pivot 
at the pole is a brass needle, which, as the globe re- 
volves, remains stationary, and thus successively points 
to the hours of the day, as the numbers which indicate 
them pass in their turn beneath it. Other particulars 
might be mentioned respecting the celestial globe, but. 
this description suffices for our present purpose. 

752. How to use the globe. We will suppose it 
to be night ; the student has his globe before him, and 
the stars shine clearly in the heavens. How shall he 
arrange his globe, so that the hemisphere that rises 
above its artificial horizon shall exactly represent the 
starry hemisphere that now glows above and around 
him r It is adjusted by the following rule. Elevate the 
pole above the artificial horizon 1 to an altitude equal to the 
latitude of the place of observation. Then find the position 
of the sun in the ecliptic on the day of observation, and bring 
this point of the ecliptic directly beneath the brass meridian. 
Now turn the index to XII, and then cause the globe to re- 
volve westward until the index points to the hour of ob- 
servation. The constellations figured on the globe are 
then situated, in respect to its artificial horizon, just as 

1. In the regions of the earth north of the equator the north pole of the 
celestial globe must of course be elevated ; and in those lying south, the 
touth pole. 

Explain ho 7» the eelestial globe is to be adjusted and used 1 



800 STARRY HEAVENS. 

the real constellations are, in regard to the true xtestial 
horizon. 1 

753. The student thus prepared commences his study 
of the heavens, and by comparing his globe from night 
to night with the skies, he will at length become fami- 
liar with the position of the constellations, and of the 
principal stars that compose them. 

754. Star Maps. On account of the expense of 
globes, various celestial atlases and charts have been 
made for those just beginning the study of the heavens, 
accompanied by explanatory text books. 2 In these 
only the most conspicuous stars are represented and 
described. For the advanced student and finished astro- 
nomer, star maps more full and elaborate are constructed 
with the utmost minuteness of detail ; all the known stars 
being laid down in them with the greatest exactness. 

755. By diligently comparing, under the guidance 
of their particular text books, these elementary charts 
with the heavens, the student soon obtains a general 
knowledge of the various constellations, and the respec- 
tive situations of the most conspicuous stars. 



CHAPTER II. 

DIFFERENT KINDS OF STARS. STELLAR MOTIONS. BINARY 

SYSTEMS. 

756. Periodical Stars. Among the fixed stars. 

1. For example, it being required to find by the globe what s#aa are 
above the horizon at Hartford, Ct., on the 12th July, 1854, at 10 o'clock 
P.M., proceed by the rule as follows. Elevate the north pole of the globe 
410 45' 59" (the latitude of Hartford) above the artificial horizon. Then 
find from the globe the place of the sun in the ecliptic at noon on this day, 
and bring this point of the ecliptic directly under the brass meridian. 
Next turn the index of the hour circle to XII, on the circumference of the 
hour circle, and lastly revolve the globe westward until the hour index 
points tc X. The hemisphere of the celestial globe above the artificial 
horizon will then faithfully represent the visible heavens at 10 o'clock, 
P.M., on the 12th of July 1854. 

2. For instance Burritt's Geography of the Heavens. An excellent and 
cheap star chart, has been published by the Society for the Diffusion of 
Useful Knowledge. 

State vhat is said of celestial charts an / maps ? What subjects are discussed ii» 
Chapter I. 



TEMPORARY STARS. 301 

several have been noticed which are subject to periodical 
fluctuations in brightness, and in one or two instances the 
star alternately vanishes and reappears ; these are termed 
periodical or variable stars. 

757. Mira. The most remarkable orb of this class, 
and which has been observed for the longest time, is the 
star Mira (o Ceti) in the constellation of the WJiale. 

Its changing splendor was first noticed by Fabricius in 
1596. It appears about twelve times in eleven years, 1 
shining then for. a space of two weeks with its greatest 
brilliancy, sometimes like a star of the second magnitude. 
It then decreases for about three months, till it becomes 
invisible to the naked eye, and so continues for the space 
of five months more; after which it increases in magni- 
tude and brightness for the remainder of its period. 

758. Algol. Another conspicuous periodical star is 
Algol in the constellation of Perseus {§ Persei). 

It generally shines as a star of the second magnitude, and 
continues so for 2d. 13h. 30m., when its splendor all at once 
diminishes ; and in about 3| hours it appears only as a 
star of the fourth magnitude. Thus it remains for nearly 
fifteen minutes, when it begins to increase, and in 3|- hours 
regains its original brightness ; passing through all these 
variations in 2d. 20h. 49m. It is the opinion of astrono- 
mers, that these fluctuations may be caused by the revo- 
lution of some dark body around this singular star, which 
intercepts a large portion of the stellar light, when 
*it is between the star and the earth. Between 30 and 
40 variable stars have been detected by different ob- 
servers, whose periods of changing brightness vary 
from a few days to many years, and the number dis- 
covered is annually increasing; so close a watch is 
kept upon the heavens by the sleepless eye of the 
astronomer. 

759. Temporary Stars. In different parts of the 

1. Its period is 33ld. 15h. 7m. By the term period is here understood 
ji general the interval that elapses from the time of the star's greatest 
splendor to the time when it is next again brightest. 

What are periodical or variable stars 1 Describe the variations of Mira a.rul JHguI ? 
What is supposed to be the cause of the variations of Algol ? How many periodical starr 
are now known "? What is said as to the lengths of their respective periods ? Is the list 
continually increasing 1 What are temporary stars 1 



302 STARRY HEAVENS. 

' heavens, stars have now and then been seen shining 
forth with great splendor, and after remaining for awhile 
apparently fixed, have gradually faded away, and to all 
appearance become extinct. These are called temporary 
stars, and differ from variable stars in this particular, 
that after once vanishing from our sight, they have 
never been certainly known to reappear from time to time. 
Perhaps when the science of astronomy is still farther 
advanced, it may be found that temporary stars, so 
called, are but in fact variable stars, of whose long 
periods of change we are yet ignorant. 

760. A temporary star is said to have been observed 
by Hipparchus, of Alexandria, in the year 125 B.C., 
which suddenly flashed forth in the heavens with such 
splendor as to be visible in the day time. 

In the year 389 A.D., a star of this class appeared in 
the constellation of the Eagle. For the space of three 
weeks it shone with the brilliancy of Yenus, and then 
died entirely away. Temporary stars of great splendor 
were likewise seen in the years 945, 1264, and 1572 
between the constellations of Cepheus and Cassiopea. 
From the circumstance that these stars appeared in the 
same region of the heavens, and also from the fact that 
the intervals of time between their epochs are almost 
equal, it has been supposed that they are one and the 
same star, which has a period of 312 years or possibly 
of 156. 

761. The appearance of the star of 1572 was very 
sudden. The renowned Danish astronomer, Tycho 
Brahe, upon returning from his laboratory to his house, 
on the evening of the 11th of November 1572, found a 
number of persons gazing upon a star, which he was 
confident did not exist half an hour before. It was 
then as brilliant as Sirius, and continued to increase 
in splendor till it exceeded Jupiter in brightness, and was 
even visible at noonday. In December of the same year 
it began to fade, and by March, 1574, had completely 
disappeared. A. temporary star of equal splendor blazed 

What may they perhaps at length be found to be ? Have temporary stars been np 
ticed only in modern time*? Describe the temporary stars observed in the years 389, 
»45, 1264, 157U and 1670 A.D. ? 



TEMPORARY STARS. 303 

forth on the 10th of October, 1604, in the constellation 
of Serpentarius, which continued visible for a year. 

Another star of this kind, though less brilliant, *?vas dis- 
covered in 1670 in the constellation of the Swan. It be- 
came invisible, and then reappeared; when after being sub- 
ject to strange variations in its light for the space of two 
years it at length vanished, and has never been seen again. 

762. The phenomenon of temporary stars has not yet 
ceased. Mr. J. E. Hind, who has distinguished him- 
self by the discovery of so many planets, detected a 
temporary star on the night of the 28th of April, 1848, 
in the constellation of Ophiuchus. From his perfect ac- 
quaintance with this region of the heavens, Mr. Hind 
was sure that, up to the 5th of April, no star here existed 
below the ninth magnitude. The star in question was 
between the fifth and sixth magnitude at the time of its 
discovery, and shone with a ruddy hue. By the 15th 
of August it had decreased to the seventh magnitude, 
and on the 23d of March, 1849, it ranked as a star of the 
eighth magnitude. In June, 1850, it could not be found. 
In 1866, a star in the Northern Crown suddenly blazed 
out to more than its usual size, appearing as an orb of 
the second magnitude, and in addition to the ordinary 
stellar spectrum, exhibited several bright lines. Within 
a week from this time it changed to a star of the fourth 
magnitude, and at the end of a month had decreased 
to the ninth. The bright lines coincided with those 
of hydrogen, and the star was supposed to be in a state 
of conflagration. 

763. By comparing the heavens with existing star- 
charts, and the ancient catalogues of stars with the 
modern, it has been found that many stars are missing. 
The class of temporary stars may therefore be much 
greater than is usually supposed, since, hitherto, it is 
only the most splendid that have attracted observation, 
and whose phenomena are recorded in the annals of 
science. 

Have any stars of this class been lately discovered ? By whom and when ? Relate 
the phenomena of these stars ? What is discovered by comparing the heavens with 
celestial maps, and the ancient catalogues of stars with the modern ? Is there reason 
for believing that the number of temporary stars is greater than is generally imagined ? 



304 STARRY HEAVENS. 

764. Double Stars. Many stars which appear single 
to the unaided eye, are found, when viewed through the 
telescope, to be in fact two distinct stars separated by a 
very small interval. Moreover, numerous telescopic stars, 
which are seen single when examined with ordinary in- 
struments, are resolved into two when observed through 
telescopes of high magnifying powers. Stars of this 
kind are termed double stars. 

76*5. Castor — Alpha Centauri — 61 Cygnt. The. 
bright star Castor is one of the finest examples of a 
double star, it consists of two stars of between the third 
and fourth magnitude within 5" of each other. Alpha 
Centauri, the nearest fixed star (Art. 735,) is also a re- 
markable double star, each of the component stars being 
at least of the second magnitude, and separated from each 
other by an interval of about 15". The star 61 Cygni, 
whose distance from the earth was computed by Bessel, 
(Art. 738,) belongs also to this class ; the individuals that 
compose it being of about the seventh magnitude, nearly 
equal in size, and about 15" from each other. 

766. Colored double stars. Many double stars 
display a beautiful variety of colors, the component stars 
being of different hues. l Thus in the case of the double 
star Iota, in the constellation of the Crab, (i Cancri,) the 
brightest of the component stars is yellow while the othei 
is blue. The double star Gamma in the constellation of 
Andromeda (y Andromedae,) presents a different varia- 
tion ; the most brilliant component being red and its 
companion green. The star Eta in the constellation 
of Cassiopea, (y Cassiopese,) displays a combination 
of a large white star with a small one of a rich ruddy 
purple. 

767. It is a singular fact that among double stars the 
larger component star is never blue, or green, while the 
smaller may be blue, green, or purple. Single stars of a 

1. These colors are sometimes the mere effect of contrast, that is, are 
complementary : but they are not always so, for in numerous cases the 
component stars are really of different colors. 

What are double stars ? Give examples'? What peculiarities in respect to the colore 
of the companion stars is observed 7 Is there only an apparent difference in color ? Gi r« 
instances of colored double stars 7 What has been noticed in regard tof the resvcctivt 
colors o^* the companion .stars 7 



NUMBER OF DOUBLE AND MULTIPLE STARS. 305 

deep red hue shine forth in various parts of the heavens, 
many of which are variable. 

768. Triple, and Quadruple or Multiple, Stars. 
When stars, which under common instruments appear 
double, are viewed through telescopes of greater power, a 
still further separation is not unfrequently effected. In 
some instances, one of the twin stars is resolved into two, 
and the combination is then termed a triple star. In other 
cases, each of the two component stars is separated into 
two ; and since all the four appear but as a single star to 
the naked eye, it is called a quadruple, or multiple star. 

769. Examples. The star Zeta in the constellation 
of the Crab, (£ Cancri,) consists of three stars ; two very 
close together, the third and smallest being most distant. 
The star Epsilon in the Lyre, (e Lyrae,) is a remarkable 
quadrujjle star. With telescopes of low power it'appears 
only double, but with the finest instruments each compo 
nent is seen as a double star. The star Theta, in the con- 
stellation of Orion, (0 Orionis,) is likewise a conspicuous 
multiple star. It consists of four brilliant stars of the 
fourth, sixth, seventh, and eighth magnitude; and two of 
these, according to Sir John Herschel, are each closely 
attended by an exceedingly minute companion star. 
The arrangement of the several component stars in this 
combination, are shown in Fig. 85. 

FIG. 85u 




THE MULTIPLE STAR THETA IN ORION. 

770 Number of Double and Multiple Stars. 

What peculiar hue is displayed by manv single stars ? What are triple and multivli 
tars? Give instances 1 



806 STARRY HEAVENS. 

"Very few stars of this kind were known previous to the 
hitter part of the last eentury. At this time Sir William 
llersehel arose, and with instruments at his command 
fa* superior to any before employed, and which his own 
genius and skill had constructed, entered this field of 
labor. An extraordinary SUC06SS crowned his exertions. 
Though he knew but Jour double stars when he com- 
menced his researches, he discovered within a few years 
more than 600, and during his life is said to have 
observed no less than 2,400 double stars. 

771. The subsequent labors of his son, Sir John ller- 
sehel, of Sir James South, and of Prof. Struve, of Rus- 
sia, have greatly increased this list. In 1883, when Sir 
John llersehel sailed for the Cape of Good Hope, in 
order to observe the celestial objects of the southern 
hemisphere, the whole number of known double stars 
was 3,340. While at the Gape this eminent astronomer 
discovered, in the space of about lour years, no less than 
2,19b' stars of this kind. The number thcreforo of 
double stows at the present time is between Jive and six 
thousand. 

STELLAR MOTIONS. 

772. Motion of the Solar System. By comparing 
the positions of three conspicuous stars ; viz., Sirius, 
Aldebaran, and Areturus, as determined by ancient ami 
modern observations, Dr. Ualloy discovered in 1717, 
A.D., (after making all due allowance for precession, nu- 
tation, &c.,) that they had changed their places in the 
heavens, since the time of Ilipparchus, 140 years B.C. 
This motion is termed their proper motion. 

The observations of succeeding astronomers have veri- 
fied these conclusions, and a huge number of stars are 
now known to have a proper motion. 

773. Prop Kit Motion op Sirius. From some pecu- 

To whom are we ohieflj Indebted for our knowledge of double and multiple stars? 

Give an account of his labors, and state how large a number of these objects be dis 
covered and observed ? What distinguished astronomers subsequently pursued these 
researches I How great was the list of double stars in 1S.'!;> ? How many were added 
by Sir John llersehel while at the Cape of (!ood Hope? What is the entire number 
at mescnt? What discovery was made by l>r. Hallcy upon com par ing the places of 
certain stars as determined by ancient and modern observation? What is this motion 
called ' Were these conclusions vcriilcd ? What is said of the proper motion of Sirius ? 



CENTRAL SUN. 307 

liarities lately observed in the spectrum of Sirius, Mr. 
Huggins has inferred that this star is receding from the 
earth with a proper motion of about 780,000,000 miles 
a year. If the transverse motion of Sirius, which has 
been estimated at 450,000,000 miles annually, is also 
taken into account, it results that this splendid orb is 
speeding through space with a yearly velocity of more 
than 100,000,000 miles. 

774 In 1783, Sir Wm. Herschel, by carefully com- 
paring the proper motions of those stars whose changes 
in situation were then best determined, came to the con- 
clusion that the sun with all its planets is actually moving 
from one quarter of the heavens toward the opposite region. 
If the solar system is now really advancing through 
space, the stars belonging to that part of the sky toward 
which it is moving will necessarily appear to us gradu- 
ally to recede from each other; while at the same time 
those which are situated in the opposite region of the 
heavens, and from which we are speeding away, will 
seem to approach each other and to close together. 

Phenomena like these were detected by Sir William 
Herschel, in the proper motion of the stars. At a point 
in the constellation of Hercules, he found that there 
had been a gradual separation of the stars, and toward 
this region he believed the solar system was advancing. 

775. The views of Herschel have been corroborated 
by the later and more extended observations of some 
of the most renowned living astronomers, and who have 
pushed their researches so far as to be able to estimate 
the speed of the solar motion. For, according to the 
computations of Struve, the sun with its train of planets 
and comets, is moving with a velocity of 422,000 miles 
a day, toward the same region in the constellation of 
Hercules which was pointed out by Sir William Herschel. 

776. Central Sun. Does the sun move in a straight 
line or in an orbit t All celestial analogies indicate the 
latter, and Madler of Dorpat Observatory, believes, from 
numerous observations which he has made, that he has 

What inference did Sir Wm. Herschel make from the proper motion of the stars 1 If 
the solar system is really advancing through space what stellar phenomena will occur, 
and why 1 Do these phenomena occur? To what point did Herschel believe the solar 
system was approaching ? Have his views been established ? State the results of modern 
researches 1 How fast does the snlar system move according to Struve 1 



308 STARRY HEAVENS. 

disco veretl the great central sun, around which not 
only our solar system but the stars themselves revolve. 
Alcyone in the group of the Pleiades is supposed to be 
this central sun. Its distance from us is so great that it 
would require 537 years for a ray of light to pass from 
this orb to the earth, and, if our sun revolves about it T 
his periodic time must be no less than eighteen millions 
of years. 

777. Without denying the possibility of this problem 
being eventually solved, astronomers at present consider 
the observations of Madler to be insufficient to warrant 
his conclusions. 

778. Binary Stars. The double stars are divided 
into two classes. First, those which are optically double,* 
the two individuals appearing under ordinary circumstan- 
ces as one object, simply, because they happen to be so. 
near to one another that we view them in almost exactly 
the same line of direction. No bond of union exists 
between them ; for one may be millions of millions of 
miles behind the other, and altogether beyond the reach 
of its influence. Secondly, double stars, which by their 
mutual attraction form distinct sidereal systems ; the com 
ponent stars revolving about each other in regular orbits. 
These, in order to distinguish them from double stars in 
general, are termed binary stars' 1 . 

779. In 1803, Sir William Herschel, first announced 
the fact of the existence of binary stars ; a discovery 
which was the fruit of 25 years assiduous and close ob- 
servation. At the present time more than 100 binary 
stars have been discovered, and the list is continually 
increasing. • 

780. Orbits — Periodic Times. The orbits of 15 

1. Thus, in looking over a city, we not unfrequently see two steeples one 
behind the other, so nearly in the same line of direction that they appear as 
one object. At the first glance the figure formed by their union may seem 
single ; a closer inspection shows that it is optically double. 

2. Binary, from the Latin binus, meaning two and two by couples. 

What are the views of Madler respecting a central snn 1 What orb does he suppose it 
to be and where situated 1 How far is this orb from the earth 7 How long would the sun 
be in revolving around it? What views are entertained by astronomers respecting Madler's 
theory ? Into how many classes are double stars divided 1 Describe these classes 7 
When and by whom was the existence of binary stars first announced 1 Of how many 
years research was this discovery the fruit 1 How many binury stars are at preseni 
known ? 



STARRY CLUSTERS. 309 

omary stars have been ascertained, and their periodic 
times with more or less certainty determined. Like the 
planets of our system they revolve in elliptical paths, and 
the correspondence that exists between their calculated, 
and observed positions in various points of their orbits, 
proves that the laws of gravitation extends to these far 
distant bodies. 1 

Their known periodic times range from 31 to 736 
years. The names of a few of the binary stars, with 
their respective times of revolution are given in the. fol- 
lowing table, 

NAME OF STAR. PERIODIC TIME 

Zeta, in the Constellation of the Hercules, (£Herculis,) 36 years, 
Alpha, " " of the Centaur, ( a Centauri,) 77 " 

Gamma, " " of the Virgin, (yVirginis,) 182 " 

Castor, " u of the Twins, (a Geminorum,) 253 " 

Sigma, " " of the Crown, (<r Coronae,) 736 " 

781. In contemplating the systems of binary stars, "we 
are not concerned," says Sir John Herschel, " with the 
revolutions of bodies of a planetary or cometary nature 
round a solar center ; but with that of sun around sun — 
each perhaps accompanied with its train of planets and 
their satellites, closely shrouded from our view bv the 
splendor of their respective suns." 



CHAPTER III. 

STARRY CLUSTERS-NEBUL^E-NEBULOUS STARS-ZODIACAL LIGHT-MA 
GELLAN CLOUDS-STRUCTURE 0E THE HEAVENS. 

782. Starry Clusters. When we turn our gaze 
upon the heavens in a serene night, we perceive that in 
some parts the stars are more crowded together than in 
others, forming by their close proximity groups or clus 

1. The calculations are made upon the supposition that these f-sdh* 
revolve about each other in obedience to the laws of universal gravitaiaon. 

Of how many have the orbits and periodic times been ascertained v'th more or less ao 
curacy? In what kind of orbits do they revolve 1 What fact shows that they are con- 
trolled in their motion by the laws of universal gravitaticn ? What is said of the extent 
of their periodic times ? Give the list ? What does Sir John Herschel ^ay respecUri^ tb» 
systems of binary stars ? Of what does Chapter III. treat 1 



310 STARRY HEAVENS. 

ters. Such a cluster is the Pleiades, in which six or 
seven stars are seen by the naked eye, but where the 
telescope reveals fifty or sixty comprised within a very 
small space. The constellation, termed Coma Berenices, 
is another stellar cluster consisting of larger stars than 
those which form the group the Pleiades. In the constel- 
lation of the Grab is a luminous spot, called the Beehive, 
which a telescope of ordinary power shows to be con 
stituted entirely of stars. In the sword-handle of Perseus 
is a similar spot, which, with a finer instrument, is re- 
vealed as two clusters of stars crowded thickly together. 

783. " Many of the stellar clusters are of an exactly 
round shape," says Sir John Herschel, " and convey the 
complete idea of a globular space filled full of stars insu- 
lated in the heavens, and constituting in itself a family 
or society apart from the rest and subject to its own in- 
ternal laws." 

The central portion of a cluster is usually most thickly 
sown with stars, and the stellar light there shines 
forth with the greatest brilliancy. A beautiful cluster 
of this kind is found in the constellation of Hercules. 
It is represented in Fig. 86. 

784. Number of Stars in a Cluster. The stars 
that compose a globular cluster are often exceedingly 
numerous. It has been estimated that not less than five 
thousand stars exist in some of the groups, wedged together 
into a space in the heavens, the area of which does not 
exceed one-tenth part of that covered by the moon. 

785. Milky Way, or Galaxy. 1 The most mag- 
nificent stellar cluster, by far, is the milky way, which 
like a broad zone of light encompasses the heavens. 
Its brightness is derived from the diffused radiance of 
myriads of myriads of stars that compose it, whose 
splendors are blended together into a milky whiteness on 
account of their immense distance from us. . 

786. In this cluster, Sir William Herschel estimated 



1. From the Greek word gala, signifying milk. 



Describe some of the stellar clusters'? What does Sir John Herschel sny in regard to 
stellar clusters'? What is the usual appearance presented by the central portion of n 
cluster? What is said respecting the number of stars they contain 7 Which is the most 
splendid stellar cluster that the heavens present ? What is its aspect, and whence is iU 
light derived ? 




311 



GLOBULAR CLUSTER OF STARS 



that, during one hour's observation with his telescope, no 
less than 50,000 stars passed before his sight within a 
zone 2° in breadth. Sir John Herschel has computed 
that the number of stars in the milky way, sufficiently 
visible to be counted, when viewed with his 20 feet tele- 
scope, amount in both hemispheres to five and a half mil 
lions. The actual number in this cluster he considers to 
be much greater, since in some parts they are so crowded 
together as to defy enumeration. Our sun is supposed 
to be one of the stars belonging to this group. 

NEBULA 

787. Scattered throughout the sky are seen, either by 
the naked eye or by the aid of the telescope, dim misty 
objects of various shapes and sizes, stationary to all ap- 
pearance like the stars themselves. These objects are 
named nebuke 1 , and are arranged under the following 

1. For the meaning of this word, see page 13 note 3. 

What observations and computations have been made which show that it contains a vast 
number of star* i What i B supposed of our sun ? What tire nebula; ? How classified 1 

u 



312 STARRY HEAVENS. 

classes ; viz., Elliptical, Annular, Planetary, 
Double, Spiral, and Irregular Nebula. 

788. Elliptical Nebula. One of the finest speci- 
mens of this class is situated in the girdle of Andromeda. 
It is visible to the naked eye, and was noticed and de- 
scribed by Simon Marius in 1612 ; and there is reason 
for believing that it was seen even as early as 995. 
This nebulae is of vast size extending over an area 15' in 
diameter. It is delineated in Fig. 87. 

FIG. 87 




NEBULA OF ANDROMEDA. 



789. Annular Nebula. A remarkable annular 
nebula easily detected with a telescope of ordinary power 
is found in the constellation of the Lyre. It has the ap- 
pearance of a flat oval ring, the central space not being 
quite dark " but appearing," says Herschel, " to be filled 
with faint nebulae, like a gauze stretched over a hoop." Ne- 
bulae of this class are very rare. Nine comprise the 
entire number. 

790. Planetary Nebulje. Planetary nebulce are so 
called from their similarity in form to planets, being either 
round or somewhat oval. Only about 25 of this class 

Give examples of elliptical and annular nebulm 7 How many of the la'ter kind hi* 
now known 1 



IRREGULAR NEBULA. 313 

have yet been discovered, and nearly three quarters of 
this number are in the southern hemisphere. 

One of the most beautiful is situated in the constella- 
tion of the Cross. It is a well denned circular figure, 
12" in diameter, looking exactly like a planet. It 
has the brightness of a star of between the sixth and 
seventh magnitude, and shines with a rich blue light in- 
clining to green. A magnificent planetary nebula is 
found in the constellation of the Great Bear. Its appa- 
rent diameter is 2' 40", and upon the supposition that it 
is at the same distance from the earth as the double star, 
61 in the Swan, the actual diameter of this nebula is 
seven times greater than the diameter of Neptune's orbit ; 
that is, more than forty thousand millions of miles. 

791. Double Nebula. A few only of these objects 
have been detected. The individuals that form them 
belong to the class of planetary, nebuke. All the varieties 
of double stars" says Herschel, " in respect to distance, 
position, and relative brightness have their counterparts in 
double nebuhe? 

792. Spiral Nebula. The discovery of a number 
of nebulae presenting the appearance of spirals or whirl- 
pools, has lately rewarded the researches of astrono- 
mers. They are a singular class of stellar objects alto- 
gether different from any before known, requiring the 
very finest telescopes to reveal their structure. For 
though the telescopes of the Herschels and other able 
astronomers had been sweeping over them for the 
space of nearly a hundred years, their true nature was 
only disclosed beneath the powerful telescopes of Lord 
Kosse 1 . 

793. Irregular Nebula. Irregular nebuhe, as 
their name implies, are entirely destitute of any regu- 
larity in form. They are of very great extent and are 
found either within the milky way or skirting its edges. 

1. The Earl of Rosse has constructed a reflecting telescope, the mirror 
of which is six feet in diameter and weighs three tons. The tube of the 
telescope is fifty-six feet in length. This instrument is the greatest, and 
the most powerful of any that has ever been constructed. 

jRive instances of planetary nebula? What i» said respecting double nebulceenii spiral 
%ebvitr * What are irregular nebula 1 



RH 



STARRY HEAVENS. 



Tne most splendid of this class is the nebula in the 
sword-handle of Orion. It consists of straggling chudlike 
spots, occupying a space in the heavens considerably lar- 
ger than the disk of the moon. This nebula was discov- 
ered by Huyghensin 1656. In Fig. 88, its central por* 



fig. sa 




NEBULA OF ORION. 

tions are shown as they have been delineated by Sir John 
Herschel. 

794. Their Constitution. Stellar clusters and nebulr 
have usually been regarded as distinct classes of celestial 
objects; the former consisting of groups of stars, either 
visible to the naked eye or through the telescope, aul 
the latter of vast collections of unformed matter diffuse* 1 

Which isoteof the most splendid"? What views have been entertained re«i>e-t njj 
stellar clusters and nebuls 1 



THEIR CONSTITUTION. 315 

through the infinitude of space. But it is by no means 
certain that such a distinction exists in nature, for the 
late discoveries of eminent astronomers point to the con- 
clusion, that the nebulae, are clusters of stars Trior e or less dis- 
tant from us. The nearest and least crowded requiring 
but ordinary telescopes to resolve them into stars ; while 
those which are farther off, and more thickly studded with 
stars, can be resolved only by instruments of greater 
excellence and power. 

795. Sir William Herschel divided nebulas into two 
great classes ; viz., those which could be separated into 
stars by the telescope, and those that could not; the for- 
mer were termed resolvable nebulas, and the latter irre- 
solvable. 

796. But since the time of this renowned astronomer 
the telescope has been wonderfully improved, and dis- 
coveries made corresponding with its higher degree of 
perfection. Nebulae, which had before been regarded as 
irresolvable, have successively yielded to the increased 
power of the telescope, and been revealed as splendid 
clusters of stars. 

797. For a long time the nebula in Orion withstood 
the highest powers of the telescope to resolve it, but 
when, during the winter of 1845, it was examined by 
Lord Kosse, in his immense telescope, it was seen bril- 
liant with vast collections of stars, proving that it was 
really a stellar cluster. 

The great nebula in Andromeda, when viewed 
through the noble instrument belonging to Harvard 
University, appears to be studded over with multitudes of 
stars, which form however no portion of the nebula. 
This object at present is regarded as unresolved. 

798. But while the augmented power of the telescope 
has resolved 'numerous known nebulce into starry groups, 
it has also brought to light from the depth of space 
many nebulae which were before invisible; for even in the 
powerful instrument of Lord Rosse misty objects before 
unseen are va\ caled as nebulce, without any sign of re- 
solvability. 

To what conclusion do the late discoveries of astronomers point? Into what two 
great classes did Sir William Herschel divide the nebulae ? What advances in thia 
field of research have been made since his time ? What has the nebulae of Orion 
proved to be ? Has that of Andromeda been resolved ? 



316 STARRY HEAVENS. 

799. Revelations op the Spectrum. Out of 70 
nebulae examined by Huggins, about one-third display 
three, or else one or two bright spectral lines, which cor- 
respond with those of oxygen and nitrogen, and per- 
haps of hydrogen ; the spectra of the rest are like those 
of the sun and fixed stars. The spectra of the first 
class indicate that they are not incandescent bodies, 
surrounded by an absorptive and luminous atmosphere 
like the sun, but that their respective surfaces consist 
of an ocean of luminous gas or vapor. Possibly many 
of these bodies are simply vast masses of glowing gas. 

800. Number and distance of Stellar Clusters 
and Nebula. About two thousand stellar clusters and 
nebulce were observed by Sir William Herschel. In 
1833 the list amounted to two thousand Jive hundred, 
and this number was increased to about four thousand 
by the splendid discoveries made by Sir John Herschel, 
during his residence at the Cape of Good Hope. The 
distance of the nebulce from the earth is vast beyond 
conception. The ring nebula in the Lyre is so remote, 
that astronomers assert a ray of light cannot reach us 
from this object in less than twenty or thirty thousand 
years. 

The nebula of Orion is still more distant, for it is 
computed that a ray of light, moving as it does with a 
velocity of 192000 miles in a second, would occupy not 
less than sixty thousand years in travelling from this nebula 
the earth. 

801. Their Physical Structure. Mathematicians 
have clearly shown it to be utterly impossible that the 
stars composing individual clusters and nebulee could 
have been so grouped together by mere chance. 1 Their 
union must consequently be the result of some physical 

1. Mitchell has shown that if 1500 stars, like the six brightest in the 
Pleiades, were scattered at random through the heavens, there would be 
only one chance out of Jive hundred thousand that any six of them would 
come as close together as they do in the Pleiades. 

What other discovery besides the separation of many nebulae into starry clusters, 
has resulted from the increased power of the telescope ? What are the revelations 
of the spectrum in regard to the nebulae ? Relate in full what is said respecting the 
number and distance of stellar clusters and nebulae 1 State what is said of our dis- 
tance from the nebula of Orion ? What is remarked in regard to the physical struc- 
ture of stellar clusters and nebulaa ? 



NEBULOUS STAES. 317 

law impressed upon them by their Creator, in virtue of 
which they are combined in harmonious systems. This 
view is strengthened, when we perceive that these clusters 
tend to assume in numerous instances distinct forms ; 
many of them appearing round like a planet, with 
their outlines sharply denned ; the component stars to- 
ward the center being often closer together than at the borders. 

802. We have therefore reason for believing that a 
stellar cluster is a celestial system composed of solar systems, 
each individual star being a sun, having its attendant 
train of planets and comets like our own. Every sun 
being separated from its brother suns by enormous inter- 
vals of space, although, owing to the vast distance at 
which we view them, they appear to us crowded and , 
■wedged together. 

803. Under the action of universal gravitation matter 
assumes a spherical shape and is the densest at the center. 
The globular form of some of the stellar clusters, and 
the closer union of the stars toward the central parts, 
point to this influence as that which unites and controls 
these starry systems, or island universes, as they have 
been aptly termed. 

804. Nebulous Stars. In various parts of the 
heavens bright and sharply defined stars are beheid en- 
veloped in a cloudlike disk or atmosphere, — these are called 

FIG. 89. 




A NEBULOUS STAR. 



Mutt their union be the result of some physical law ? What facts strengthen this 
riewt What have we reason for believing? What i6 the influence which probably 
— and controls these starry systems 1 What are nebulous stars 7 

27* 



318 STARRY HEAVENS. 

nebulous stars. In some cases this hazy envelope is cir* 
cular in form, with the star situated in the center, in 
others it is elliptical; and there are instances where the 
nebulous atmosphere has no definite boundary, but 
fades away by degrees in every direction. The ap- 
pearance presented by a nebulous star is shown in 
Figure 89. 

805. Zodiacal Light. The zodiacal light is a lumin- 
ous object shaped like a pyramid, that accompanies the 
sun in his apparent course through the heavens. 

806. Aspects. According to Prof. Olmsted, who has 
made this phenomenon an especial study, the zodiacal 
light, in our climate, becomes visible in the eastern sky 
about the beginning of October. It is then seen before 
the dawn, its base resting upon that part of the horizon 
where the sun at this time rises, the luminous pyramid ex- 
tending, obliquely upward, until its point reaches above 
the starry cluster of the Beehive, in the constellation of 
Cancer. Throughout the month of December it is beheld 
on both sides of the sun, being seen in the morning before 
sunrise, and in the evening after sunset, extending in the 
first case sometimes as far as 50° westward from the sun, 
and in the second 70° eastward. In February and 
March the zodiacal light appears only in the west after 
sunset; it is then most conspicuous, and its luminous 
point is seen as far up as the Pleiades. 

807. Size. This object possesses no well defined out- 
line, but its light gradually fades away from the central 
to the outer portion, until it becomes too faint to be dis- 
cerned. Its breadth at the base varies from 8° to 30° ac- 
cording to Herschel, but Prof. Olmsted has noticed it 
when it was 40° in width. 

From the observations of the latter gentleman it ap- 
pears, that the zodiacal light sometimes extends in length 
considerably beyond the orbit of the earth; for on 
the 18th of December, 1837, it was beheld stretching 
away eastward from the sun to the distance of 120°. 

807. Nature. Sii John Herschel conjectures that 
the zodiacal light is an elongated oval shaped envelope, en- 

Htnte their varioui aspects ? What is the zodiacal light ? What are its aspect in out 
» mate ? Whm is stated respecting the size of the zodiacal light 1 



MAGELLAN CLOUDS. 319 

closing the sun, consisting of extremely light matter, and 
possibly composed to a great extent of the same materi- 
als which form the tails of comets. Under this view, 
the sun surrounded by the zodiacal light presents a phe- 
nomenon similar to that of the nebulous stars. 

809. Professor Olmsted, whose opinions on this sub- 
ject are entitled to great weight, believes that the zodia- 
cal light is a nebulous body which revolves about the 
sun, and is probably the cause of the splendid meteoric 
showers that occur from time to time. 

810. Magellan Clouds. This name has been given 
to two vast luminous objects, clearly visible to the naked 
eye in the southern hemisphere, and similar in appear- 
ance to the Milky Way. They differ in size, the smallest 
being the brightest, but both of them possess an oval 
form. 

811. These chudlihe tracts, when examined through 
telescopes of great power, are found to be composed of 
separate stars, stellar groups and nebuke. Among the 
stellar groups are globular clusters with their component 
stars more or less crowded together, while the nebulce 
exhibit in profusion every variety found in other parts 
of the heavens, and in addition some which are peculiar 
to this region. 

812. Within the larger of the Magellan clouds no 
less than 278 clusters and nebulas have been discovered, 
while on the outskirts from 50 to 60 more are seen. 
The smaller contains 37 of these objects and 6 others are 
found upon its borders. 

813. The Nebular Hypothesis. This hypothesis 
seeks to explain in what manner the solar system, and 
perhaps other systems, were formed by the operation 
of the known laws which the Creator has impressed 
upon matter. 

814. The Hypothesis Stated. According to the 
nebular hypothesis, the whole amount of matter which 
forms the solar system was once a nebulous mass, that 
extended far beyond the orbit of the most distant 

What are the views of Sir John Herschel in regard to its nature ? What are those 
of Prof. Olmsted ? Describe the Magellan clouds ? What does the nebular hypoth- 
esis propose to explain ? State this hypothesis ? 



320 STARRY HEAVENS. 

planet. This mass was in a highly rarefied and in- 
tensely heated condition, and had a slow motion of ro- 
tation on its axis in a direction now termed from west 
to east. By the action of gravity, combined with the 
centrifugal force, the nebula would, of necessity, as- 
sume a spherical shape. As it gradually cooled by 
the loss of heat from radiation, it would contract in 
its dimensions, and this diminution in size would be 
attended with an increase in the centrifugal force. 
At length a point of contraction would be reached 
when the centrifugal force at the equatorial regions 
would be just equal to the opposing force of gravity, 
and under these circumstances, the equatorial part 
would revolve as a ring about the interior mass, 
and independently of the latter. The central mass 
continuing to contract, would throw off successively 
an indefinite number of concentric nebulous rings 
in the plane of the equator. These rings or zones 
would mainly revolve from west to east, and with a 
greater velocity as they were nearer the central mass, 
which would continue to diminish in bulk and in- 
crease in density. The central mass is the sun of the 
system. 

815. Nebulous Zones changed into Planets. The 
detached rings revolving about the sun would cool 
and contract like the central mass, but unless the 
amount of matter in a ring was uniformly distributed 
throughout, which would rarely happen, it would be 
drawn to the heaviest side, and form a spheroid rotating 
on its own axis, while it revolved also around the sun. 
Their respective directions would, on the whole, be from 
west to east, but the outer bodies might move in a 
contrary direction. If at any time a number of small 
rings were detached, or a large one broken up into 
many separate portions, a group of planetoids might be 
produced. Thus from the original nebula, a sun with 
its planetary system would be formed. 

How are the nebulous rings supposed to be changed into planets ? How are sec- 
ondary rings and moons imagined to be formed ? 



NEBULAR HYPOTHESIS. 321 

816. Secondary Rings and Moons. Each of the 
planetary masses, as they cooled and contracted, might, 
like the central body, throw off successively rings of 
their own. These would gather into spheroids, like 
the primary rings, and at last revolve as moons around 
the planetary mass to which they belonged, and in the 
same direction. If the matter composing any second- 
ary ring was very nicely adjusted, its original form 
might remain unchanged. 

817. Physical Condition of the Bodies op the 
System. Each planet and satellite formed from the 
nebulous mass cooling by radiation, would at length 
cease to shine by its own light, and would gradually 
assume the liquid or solid state, but in the latter case 
the solidity might be only partial, a solid outer crust 
or shell being formed, while the interior remained in 
a fluid state, or in a highly heated condition. 

818. Coincidences Existing Between the Hypo- 
thetical Nebular System and the Solar System. 
The hypothetical nebular system consists of a sun with 
planets and moons, or in rare cases, rings in the place 
of moons. The solar system is formed of the like 
bodies, having, one ring, that of Saturn, while there 
are 19 moons. All the planets of the former, with 
their moons, must revolve about the central body in 
the same direction, and all the moons must rotate in 
the same manner as their primaries. This law ob- 
tains in the solar system, since Neptune and Uranus 
constitute the only exceptions, their satellites having 
a retrograde motion, and the planets themselves per- 
haps having the same. The planets of the imaginary 
system would have the planes of their orbits but 
slightly deviating from that of the solar equator. The 
planets of the solar system observe this law. Planet- 
oids might be formed according to the nebular hy- 
pothesis. Planetoids occur in the solar system. In 
the former the density of the planets would diminish 

What would be the physical condition of the bodies of a nebular system ? State 
the coincidences existing between the supposed nebular system and the solar 
system? 



322 STARRY HEAVENS. 

with their distances from the central mass. In the 
latter this is generally the case. 

In the nebular hypothesis, the bodies of the system, 
in their physical aspects, pass by successive stages 
from the condition of an intensely heated gas into a 
liquid and solid state, the indications of heat being 
everywhere present. In the solar system, the sun is 
an intensely hot body, enveloped in an atmosphere of 
metallic vapors. The interior of the earth is in a 
state of fusion from heat, as is proved by the rivers 
of melted rock thrown out by volcanoes ; and the sur- 
face of the moon is covered with extinct volcanoes 
and lava plains. These coincidences give much prob- 
ability to the nebular hypothesis in respect to the 
formation of the solar system. The cometary bodies 
of the solar system may be regarded as nebulous 
bodies which the sun meets in its progress through 
space, and compels by its attractive force to revolve 
around it. 

819. Origin op the Fixed Stars. Every single 
fixed star, like our sun, may be the residual nucleus 
of a once vast nebulous body, and the double and 
triple stars may present instances where the original 
body separated into two or three immense masses be- 
fore the contraction had proceeded far. In the true 
nebulae of regular form, unresolvable into stars, we 
may perhaps be viewing a solar system in a state 
of formation, and the bright lines in many of these 
indicating the presence of gaseous matter intense- 
ly hot, increases the probability of the nebular hy- 
pothesis. 

What inference is drawn from these coincidences ? In what light may cometary 
bodies be regarded ? What is said of the origin of the fixed stars, both single and 
multiple ? What may be the condition of the true nebulae ? Does the spectrum 
analysis favor this hypothesis ? 



SUMMARY OP THE HISTORY OF ASTRONOMY. 323 



CHAPTER IV. 

SUMMARY OF THE HISTORY OF ASTRONOMY. 

820. Ancient Astronomy. The science of Astron- 
omy was cultivated at a very remote period by the 
Chinese, Egyptians', and Chaldeans, and perhaps by the 
Hindoos. The knowledge they acquired of the heavenly 
bodies, was simply the result of diligent and continued 
observations, for astronomical instruments, except the 
rudest, were then unknown, yet this knowledge sufficed 
for the construction of tables of the celestial motions, 
by the aid of which eclipses could be predicted, and 
other celestial phenomena ascertained. 

821. Chinesr Astronomy. The Chinese appear to 
have been the first of the. ancient nations that culti- 
vated astronomy. Fohi, the first emperor of China, 
who reigned 2752 A. C, constructed astronomical tables 
and instituted sacrifices at the times of the solstices. 
At a very early period the pole star was known, and 
a table of the daily motion of the five then known 
planets constructed. About 300 years A.C. , the Chinese 
fixed the length of the tropical year at 365J days, and 
their determination of the obliquity of the ecliptic is 
true within about 12'. In 104 A. C, rules were given 
by two Chinese astronomers for calculating eclipses 
and the motions of planets. This nation, in the second 
century before the Christian era, possessed a catalogue 
of 2,500 stars, and was acquainted with many impor- 
tant astronomical facts beside those which have been 
mentioned. 

822. Egyptian Astronomy. The ancient Egyptians 
first fixed the length of the tropical year at 365 days, 
and in all probability by observing the interval between 

What is said respecting the antiquity of the science of astronomy ? How did the 
ancients obtain their astronomical knowledge? For what did it suffice? Give an 
account of the astronomy of the Chinese, and of the Egyptians ? 



324 HISTORY OF ASTRONOMY. 

two successive days when Sirius (called by them 
Sothis,) rose with the sun. This event occurred 
about the time of the annual swelling of the Nile. 
They afterward discovered that by reckoning the 
length of the year at 365 days, Sirius rose six hours 
later every year, which led them to make the length 
of the year 365J days. They still, however, retained 
the first computation, and by making the two different 
years begin together, formed the Sothic period. (Art. 
140.) The Egyptians believed that the earth was im- 
movable, and that the sun and moon, together with 
Mars, Jupiter, and Saturn, revolved about it. Mercury 
and Venus they supposed to revolve around the sun, and 
to be carried along with the latter in its motion around 
the earth. They were aware of the direct and retro- 
grade motion of the planets. They considered the 
earth to be spherical, and that the moon was eclipsed 
by falling into its shadow. The sun they regarded as 
moving in a direction contrary to its diurnal motion, 
and in a circle inclined to the ecliptic. They divided 
the Zodiac in the same manner as the Chaldeans, and 
reckoned from the first of Aries. 

823. Chaldean Astronomy. When Alexander took 
Babylon, 331 A.C., Callisthenes,a Greek philosopher, is 
said to have found Chaldean astronomical tables which 
extended to 19 centuries before that time. Some 
doubt has, however, been thrown upon this statement. 
The Chaldeans grouped the stars into 36 constella- 
tions, 12 of which they placed in the Zodiac. Their 
determination of the respective lengths of the tropical 
year, and of the sidereal and synodical months, is cor- 
rect within a very few seconds. Their knowledge of 
the Saros (Art. 381,) has already been mentioned, as 
well as their observation of eclipses (Art. 359,) and 
of the planet Saturn (Art. 569). 

The Chaldeans were acquainted with other impor- 
tant astronomical facts, and their interest in the science^ 
of astronomy is shown by their sending an embassy 

Give an account of the astronomy of the Chaldeans ? 



GREEK ASTRONOMY. 325 

to Jerusalem, in the year 712 A. C, to enquire of 
Hezekiah respecting the sun's shadow going back on 
the dial of Ahaz. 

824. Hindoo Astronomy. A very high antiquity 
has been claimed for the astronomy of India, for the 
astronomical tables of the Hindoos, according to some 
philosophers, are based on observations which were 
made more than 3000 years before the Christian era, 
but others assign to them a more recent origin. 

The Hindoos were acquainted with the precession of 
the equinoxes, and made the annual change 54'. Their 
determination of the obliquity of the ecliptic differs 
but a little from the true value ; while the length of 
the Hindoo tropical year is correct within about 2'. 
They also knew that the moon revolves on her axis 
once every lunar month, and their length of a luna- 
tion is correct with less than 2'. The Hindoo sidereal 
periods of Mercury, Mars, and Jupiter, agree exactly 
with those of modern science, while the difference is but 
a few days in the cases of Venus and Saturn. Eclipses 
were computed by the Hindoo tables, but the errors 
were large, the actual duration of an eclipse sometimes 
varying from the computed time by more than half an 
hour. They placed the earth in the centre of the 
world, and supposed the other known planets to re- 
volve around it. 

825. Greek Astronomy. The Greeks derived their 
knowledge of astronomy from the Egyptian and Chal- 
dean, but advanced further than their teachers. 

The earliest Greek astronomer was Thales of Miletus, 
who flourished about 640 years before Christ. He held 
that the earth was spherical, and that the moon was 
eclipsed by falling into the earth's shadow. He divid- 
ed the earth into five zones, and knew of the obliquity 
of the ecliptic to the equator. Thales was the first 
among the Greeks who successfully predicted an 

What is said respecting the antiquity of the Hindoo astronomy ? State what was 
known by the Hindoos ? Whence did the Greeks derive their astronomy ? Did they 
advance the science ? Who was the earliest Greek astronomer ? When did he flourish 
and what did he know ? 



326 HISTORY OP ASIRONOMY. 

eclipse. The next distinguished Grecian astronomer 
was Pythagoras, who was born at Samos 550 years 
before Christ. After studying for about 37 years in 
Egypt and Chaldea, he established a celebrated school 
at Crotona. This philosopher held that the sun was 
the centre of our system, around which the planets 
revolved, and that the earth revolves daily on its axis 
and yearly around the sun. He believed that the fixed 
stars were suns, the centres of systems like our own, 
and that the galaxy was an assemblage of fixed stars. 

Pythagoras knew that the earth was round, that 
its surface was naturally divided into five zones, and 
that the plane of the ecliptic is inclined to that of the 
equator ; and he is regarded as the first astronomer 
who taught that the morning and evening star were 
one and the same planet. This astronomer was also 
acquainted with the principal constellations, and knew 
the causes of eclipses and the mode of predicting them. 
The views of Pythagoras in regard to the system of 
the world were in the main correct, but they were re- 
jected by all succeeding astronomers until the time of 
Copernicus, which was about 2000 years afterward. 
Philolaus, a disciple of Pythagoras, was persecuted 
and obliged to fly his country for teaching that the 
sun was the centre of our system. 

826. Endoxus, a scholar of Plato, flourished about 
360 years A. C. He rejected the theory of Pytha- 
goras, and substituted that of Crystalline Spheres. Ac- 
cording to this system all the heavenly bodies are set 
in crystal orbs, perfectly transparent. The sun and 
planets have each a separate orb, while the fixed stars 
are set in one vast orb, beyond which is another called 
the Primum Mobile, which has a daily motion from 
east to west, and carries with it all the other orbs in 
the same direction. The planetary and solar motions 
are explained on the supposition that each of these 

Give an account of Pythagoras ? What were the views which this philosopher 
held in regard to the system of the world ? Were these views accepted hy succeed- 
ing astronomers ? What is said of Philolaus ? Who was Endoxus ? What did he 
believe ? Give an account of the system of Crystalline Spheres ? 



ALEXANDRIAN SCHOOL. 827 

bodies has a motion of its own from west to east, as 
well as an opposite motion, due to the Primum Mobile. 

827. Alexandrian School. This famous school of 
astronomy was founded at Alexandria in Egypt, about 
300 years before Christ, and for several centuries was 
fostered by the munificent patronage of the Egyptian 
kings. It was during this period that instruments for 
measuring angles were used in astronomical observa- 
tions, and a more accurate knowledge of the celestial 
motions obtained than had been gained in previous 
ages. 

Among the distinguished men belonging to this 
school are Aristulus, Trinocharis, Eratosthenes, Hip- 
parchus, and Ptolemy. Aristulus and Trinocharis 
made observations on the planets and stars in order 
to determine their positions, and Eratosthenes deter- 
mined the obliquity of the ecliptic, and measured the 
circumference of the earth (Art. 25). ButHippar- 
chus and Ptolemy were the great luminaries of this 
school. 

828. Hipparchus. Hipparchus was born at Nice, 
and flourished about 140 years A. C. He was the first 
philosopher who cultivated every part of astronomy, 
and his researches were very extensive. He verified the 
amount of the obliquity of the ecliptic, as fixed by 
Eratosthenes, discovered the precession of the equi- 
noxes, and determined the length of the tropical year 
with surprising exactness (Art. 138). He ascertain- 
ed with great accuracy the various lunar motions and 
the inclination of the plane of the moon's orbit to 
that of the ecliptic. This astronomer noted the re- 
spective latitudes and longitudes of 1,022 fixed stars, 
together with their apparent magnitudes. He was the 
first philosopher who fixed the position of places on 
the earth by means of latitude and longitude, the 
standard meridian passing through Ferro, one of the 

State what is said of the Alexandrian School? What eminent men belonged to 
it ? What were the labors of Aristulus, Trinocharis, and Eratosthenes ? Who were 
luminaries of this school? Give an account of Hipparchus, and of his research in 
astronomy ? What progress was made in the science immediately after Hipparchus ? 



328 HISTORY OF ASTRONOMY. 

Canary Isles. He also indicated the method of de- 
termining terrestrial longitudes by means of lunar 
eclipses ; and in the course of his labors was led to 
investigate the nature of plane and spherical triangles. 

829. Ptolemy. Little or no progress was made in 
astronomy from the time of Hipparchus to the first 
century of the Christian era, when Ptolemy arose, who 
continued the plan begun by Hipparchus, of reforming 
the science of astronomy. He collected all the astro- 
nomical knowledge which had been preserved either 
by history or tradition, and this, together with the re- 
sults of his own researches, is preserved in his Alma- 
gest ; a great treatise which continued for ages to be the 
work by which every nation in Europe, and even many 
in Asia, were instructed in the science of astronomy. 

Ptolemy detected the equation.of the moon, termed 
her evection, confirmed the discovery of Hipparchus 
of the precession of the equinoxes, and ascertained 
the longitudes of many of the stars. He also had a 
knowledge of the effect of refraction, and understood 
the projection of charts ; but he is chiefly distin- 
guished for having elaborated, from the materials at 
his command, that system of the world which is known 
as the Ptolemaic System. 

830. Ptolemaic System. According to this system 
the earth is the centre of the universe, and all the 
heavenly bodies revolve daily about it from east to west. 
But the planetary motions are sometimes in this direc- 
tion and sometimes in the opposite, and these changes 
were explained by supposing that in the circumference 
of a circle which had the earth in the centre, moved 
the centre of another small circle in whose circum- 
ference the planet revolved. The first circle was called 
the deferent, and the small one the epicycle. The cen- 
tre of the epicycle was supposed to move from west to 
east, and the deferent from east to west. 

When did Ptolemy flourish ? What plan did he pursue in respect to the science 
of astronomy? What is the Almagest? What is said of it? Give an account of 
Ptolemy's labors ? What system of the world did he construct ? Describe the Ptole- 
maic System ? 



ARABIAN ASTRONOMY. 329 

831. The System untrue. The planetary motions 
could be tolerably represented by this system, which 
however is but a mere hypothesis. It is seen to be 
utterly untenable when we consider the incredible 
velocity which it assigns to the fixed stars, which, 
though at such immense distances that in some cases 
it requires hundreds of years for their light to reach 
us, must nevertheless revolve, according to this system, 
through a space equal to more than six times these 
distances in twenty-four hours. With such velocities 
the centrifugal force would be so great that it would 
be impossible for the earth, as their central body, to 
keep them in their orbits by its attractive force. 

832. Arabian Astronomy. Under the Arabian 
caliphs much attention was paid to astronomy, and 
several distinguished men flourished who cultivated 
the science with success. The obliquity of the eclip- 
tic, and the length of the year were determined with 
great exactness by Thebit Ibn Chora, and Albategnius, 
the most distinguished of all, ascertained very ac- 
curately the obliquity of the ecliptic and the precession 
of the equinoxes ; he also constructed tables for the 
moon and planets, more correct than those of Ptolemy. 
The study of astronomy was likewise pursued by the 
Arabs of Spain, and Alhazen, in the eleventh century, 
discovered the cause of the twilight, computed the 
height of the atmosphere to be 52 miles, and explain- 
ed atmospheric refraction and the method of deter- 
mining it. Western Europe received its knowledge 
of astronomy from the Spanish Arabs, and Alphonso 
X of Castile, in the 13th century, founded, for the ad- 
vancement of the science, a college at Toledo, where 
he assembled beneath his patronage all the learned 
Arabs of Spain. By their united labors astronomical 
tables were constructed superior to those of the Alex- 
andrian school. 

833. Persian Astronomy. In the 13th century, a 

Why is this system false? Give an account of the cultivation of astronomy by 
the Arabs ? What is stated respecting astronomy among the Persians and Tartars ? 



3C0 IlIriTvKiY QV A T.iOXoMY. 

descendant of Zinghis Khan established at Maragha, 
the capital of Media, a magnificent observatory. En- 
couraged by his patronage many astronomers assem- 
bled at this city, and were united into an academy 
which long flourished in Persia. Nassir Eddin, who 
had the charge of this observatory, made many obser- 
vations and composed astronomical works. 

834. Tartar Astronomy. In the 15th century Uleigh 
Beigh, a grandson of Tamerlane, pursued with devo- 
tion the study of astronomy. He established a society 
in his capital for the advancement of this science, and 
erected costly instruments for astronomical observa- 
tions. He formed a new catalogue of stars, and con- 
structed astronomical tables, nearly as accurate as 
those that were afterward calculated by Tycho Brahe. 

MODERN ASTRONOMY. 

835. Copernicus. The false views of Ptolemy in 
respect to the system of the world, prevailed until the 
beginning of the 16th century, when Copernicus arose, 
who revived the true system which had been taught by 
Pythagoras and Philolaus. 

Observing the sun, moon, and planets by the aid 
of instruments superior to those ever before used, 
he found that there was no correspondence between 
their observed places, and those which were computed 
by the tables of Ptolemy. So insuperable were the 
difficulties which encountered him, that he at length 
rejected the Ptolemaic system as false, and gave to 
the world the Copernican system, which his own re- 
searches as well as those of succeeding astronomers 
have indisputably shown to be the true system. 

836. Copernican System. This system maintains, 
first, that the apparent diurnal motions of the heavenly 
bodies from east to west, are caused by the actual revo- 
lution of the earth on its axis from west to east ; and 

How long did the system of Ptolemy prevail ? Who was Copernicus? What did 
he do for astronomy, and why? Explain the Copernican System? Why is it the 
true system ? 



TYCHONIC SYSTEM. 331 

secondly, that the sun is the centre around which the 
earth and the rest of the planets revolve. 

This system is not a mere hypothesis. The fact of 
the earth's rotation is established by several proofs 
which have already been given in chapter first. The 
phases of Mercury, Venus, and Mars, and the phe- 
nomenon of the aberration of light prove that these 
planets and the earth revolve about the sun, and we 
are led by analogy as well as by other reasons, to infer 
that the rest of the planets have the same centre of 
motion. Moreover, this system is in entire accordance 
with the great law of gravitation in all its refined ap- 
plications. 

837. Tycho Brahe. Astronomy is much indebted 
to the genius of Tycho Brahe, who was born at Kmid- 
strop in Norway, 1546. He was remarkable for his 
great practical skill, and constructed instruments for 
the measurement of angles of 10", while the ancient 
astronomers could measure only 10' of arc. For 
more than twenty years Tycho studied the heavenly 
bodies with untiring assiduity, and amassed a vast 
number of observations which were of the greatest use 
not only to himself but succeeding astronomers. He 
rejected, however, the Copernican system, and pro- 
pounded one of his own. 

838. Tychonic System. According to this system 
the earth is stationary in the centre of the universe, 
and all the heavenly bodies revolve ^about it from east 
to west, in the space of twenty-four hours.. The planets 
and comets are supposed to revolve about the sun, 
which together with these bodies revolves around the 
earth in the course of a year, in the same manner as 
Jupiter and his satellites revolve about the sun. This 
system explained the phenomena of the heavens, but it is 
subject to the same objections as the Ptolemaic system. 

839. Progress op Astronomy under Kepler, Gali- 
leo, and others. Kepler, a man of rare endowments 

Give an account of Tvcho Brahe and his labors? Explain the Tychonic System? 
Why is it not true ? Who was Kepler, and what discoveries did he make ? 



332 HISTORY OF ASTRONOMY. 

of mind and great eccentricity of character, was the 
friend and fellow laborer of Tycho Brake. He de- 
voted kimself for years, witk extraordinary diligence, 
to the study of the planetary motions, making use of 
his own and of r l ycho Brake's observations, and at 
length discovered those three great laws which bear 
his name. (Art. 193.) Contemporary with Kepler 
was Galileo, an Italian philosopher, to whose genius ' 
we are indebted for the invention of the telescope, 
which gave a wonderful impulse to the science of as- 
tronomy. By the aid of this instrument numerous 
celestial discoveries were made by Galileo, and among 
the most important was that of the satellites of Jupiter, 
which presents the true system of the world in minia- 
ture. All the researches of Galileo proved the truth 
of the Copernican system, which he fully believed, and 
for his adherence to this he was persecuted by the 
Romish Church, which regarded this system as con- 
trary to Scripture. 

840. During the life of Galileo, and in the period 
immediately after, several astronomers flourished who 
contributed much to the progress of the science. Among 
these may be mentioned Horrox, Crabtree, Schiener, 
Gassendi, Hevelius, Huyghens, Cassini, and Roemer. 
Hevelius was one of the best practical astronomers of 
his age, and his observations were numerous and im- 
portant. Huyghens discovered the ring of Saturn 
and one of its moons ; and Cassini, amid his other 
discoveries, ascertained the rotation on their axes of 
several of the planets, and studied with success the 
satellites of Jupiter and Saturn. To Roemer we are 
indebted for our knowledge of the velocity of light. 

841. Newton — Halley — Bradley. The illustri- 
ous Newton was born at Woolsthorpe, Lancashire, 
December 25th, 1642. To him we are indebted for 
the discovery of the great law of universal gravitation, 

Who was Galileo ? What invention of his gave a great impulse to astronomy ? 
What is said respecting his discoveries and researches? State the progress of the 
science in this age? What great law did Newton discover? What is said of its im- 
portance ? t 



RECENT PROGRESS OF ASTRONOMY. Odd 

which applied by himself and succeeding astronomers 
to the explanation of celestial phenomena, completely 
accounts for the motions of the heavenly bodies on the 
theory of Copernicus, and has established his system 
on an immovable basis. The most eminent of the 
contemporaries of Newton was Dr. Halley, who was a 
most indefatigable astronomer, and the first who suc- 
cessfully predicted the return of a comet — the one 
which still bears his name. 

Bradley, the successor of Dr. Halley as Astronomer 
Koyal at Greenwich observatory, discovered the aber- 
ration of light and the nutation of the earth's axis. 
Aberration is an apparent displacement of the fixed 
stars, and arises from the motion of light combined 
with the motion of the earth in its orbit. 

842. Recent Progress of Astronomy. In the latter 
part of the 18th century many distinguished philoso- 
phers arose, whose solid and bzilliant achievements 
greatly advanced the science of astronomy. Lacaille 
made an extensive catalogue of the stars, and his labors, 
together with those of Boguer, Condamine, and Mau- 
pertuis, were of great importance in determining the 
true figure of the earth. 

843. Euler, Clairaut, D'Alembert, LaGrange, and 
Laplace, brought all the resources of mathematics to 
bear upon the most intricate problems in astronomy, 
and solved them all with complete success on the prin- 
ciple of universal gravitation. During this period the 
solar parallax was determined with an accuracy before 
unknown. 

844. The researches of Sir William-, Herschel, which 
began by the discovery of Uranus in 1781, opened a 
brilliant era in the history of astronomy, which has 
not yet ended. By the aid of powerful telescopes, con- 
structed by himself, he sounded the depths of the 
heavens and discovered a vast number of double stars, 

For what was Halley distinguished ? What did Bradley discover ? Give an ac- 
count of the progress of astronomy under Lacaille, Euler, LaGrange, Lal'lace, and 
others ? What is said of the discoveries of Sir William Herschel ? What was hia 
theory of the sun ? 



oo4 HISTORY OF ASTRONOMY. 

nebulae, and nebulous stars. He also studied the na- 
ture of tho sun, and regarded it as a dark solid bod//, 
surrounded at a considerable distance by a stratum of 
cloudy matter, above which and nearest to us floats an 
intensely hot and luminous atmosphere. Whenever 
these two envelopes, the cloudy and the bright, arc agi- 
tated by any causes existing in the sun, they are sup- 
posed to be frequently rent asunder, and that we then 
perceive through the opening the dark body of the sun. 
Under these circumstances a spot appears. The black 
portion of the sun disclosed, is the nucleus of the spot, 
and the portions of the cloudy stratum illumined by 
the light from the luminous canopy form the penumbra. 

This theory was generally regarded as presenting 
the best explanation of the physical phenomena of the 
sun, until the surprising discoveries of Kirehoff and 
Bunsen changed the views of astronomers. 

The stellar researches of Sir William Herschcl were 
continued in the present century by his son, John F. 
W. Ilerschel, not only in Europe but also in the South- 
ern hemisphere, and the boundaries of stellar astron- 
omy were thus greatly enlarged. Within this era the 
planet Neptune has been discovered, and more than a 
hundred asteroids. The parallaxes and distances of 
many of the fixed stars have also been determined, 
and we are now learning, by means of the spectrum 
analysis, the physical nature of the sun and stars, and 
of all those forms of matter that shine upon us from 
the remote depths of space. 

What is said of the researches of John V W. Hcrschel and others ? U hat planets 
hnvc been discovered during the present century 7 What elements of many of the 
fixed stars have been determined? What are wo now learning by means of the 
spectrum analysis ? 



ASTRONOMICAL PROBLEMS. 335 



Although not in strict accordance with the plan of this 
work, it has been thought that a few astronomical problems 
might not be unacceptable to those students who possess a 
knowledge of Plane and Spherical Trigonometry. On this 
account the following problems have been prepared. 

ASTRONOMICAL PROBLEMS. 

Of four quantities, viz.: the sun's longitude, declination, 
right ascension, and the obliquity of the ecliptic, any two being 
given to find the rest. 

(1) 




In figure 1, let EC represent the ecliptic, EO the equa- 
tor, and P the pole of the equator. Let A be the place of 
the sun, and PAD the arc of a great circle passing through 
the pole and the sun. Then EAD is a right-angled spherical 
triangle, right-angled at D, and AD is the sun's declination,^ 
AE its longitude, ED its right ascension, and AED the obli- 
quity of the ecliptic. Any two of these quantities being given 
the rest can be found by Napier's rule. 

I. Given, the sun's longitude and the obliquity. Required, 
the right ascension and declination. 

Problem 1. If the sun's longitude is 30° 27' 42", and 
the obliquity of the ecliptic 23° 27' 42'; what is the right 
ascension and declination? 
15 



336 ASTRONOMICAL PROBLEMS. 

By Napier's rule, RxSin. ADz=Sin. AExSin. AED. 

R, 10. 

Sin. 30° 27' 42", 9.704975 

Sin. 23° 27' 42", 9.600031 

Sin. AD, declination (11° 38' 40"), 9.305006 

' i (Declination, 11° 38' 40". 

Ans *| Right Ascension, 28° 20' 52". 

Prob. 2. If the sun's longitude is 40° 45', and the obli- 
quity of the ecliptic 23° 27' 20"; what is its right ascension 
and declination? 

A i Declination, 15° 03' 341". 

^ ns * \ Right Ascension, 38° 19' 29''. 

II. Given, the obliquity of the ecliptic and the sun's right 
ascension. Required, the declination and longitude. 

Prob 1. The obliquity of the ecliptic being 23° 27' 29", 
and the sun's right ascension 69° 30'; what is its declination 
and longitude? 

By Napier, RXSin. ED=Tang. ADxCot. AED 

Cot. 23° 27' 29'', 10.362568 

R., 10. 

Sin. 69° 30', 9.971588 

Tang. AD (22° 7' 12"), 9.609020 

A (Declination, 22° 7' 12". 
Ans * X Longitude, 71° 4' 08". 

Prob. 2. If the obliquity of the ecliptic is 23° 27' 25", 
and the ,right ascension of the sun 55° 20' 20 "; what is its 
declination and longitude? 

A ( Declination, 19° 38' 32". 
Ans> X Longitude, 57° 36' 51". 

III. Given, the obliquity of the ecliptic, and the sun's decli- 
nation. Required, the longitude and right ascension. 

Prob. 1. The obliquity of the ecliptic, on the 31st of 
May, 1855, was 23° 27' 36'' and the declination of the sun 
21° 52' 56"; what was its longitude and right ascension? 



ASTRONOMICAL PROBLEMS. 337 

By Napier's rule, RxSin. AD=Sin. AEXSin. AED. 

Sin. 23° 27' 36", 9.600002 

R., 10. 

Sin. 21° 52' 56", 9.571360 

Sin. AE (69° 25' 9"), 9.971358 

A (Longitude, 69° 25' 9". 

j Ans * ( Right Ascension, 67° 44' 20". 

Prob. 2. The obliquity of the ecliptic, on the 8th of Sep- 
tember, 1857, being 23° 27' 38'', and the declination of the 
sun 5° 58' 8"; what is its longitude and right ascension? 

A f Longitude, 15° 8' 30". 

Ans * (Right Ascension, 13° 56' 27". 

IV. Given, the sun's right ascension and declination. Re- 
quired, the longitude and the obliquity of the ecliptic. 

Prob. 1. The right ascension of the sun being 41° 3' 54", 
and its declination 15° 54' 45"; what is its longitude, and the 
obliquity of the ecliptic? 

To find the obliquity. By Napier, RX Sin. ED=Tang. AD 
XCot. AED. 

Tang. 15° 54' 45", 9.454988 

R., 10. 

Sin. 41° 03' 54", 9.817510 

Cot. AED (23° 27' 37"), 10.362522 



A ( Obliquity, 23° 27' 37". 
. ' (Longitude, 43° 31' 30". 



The learner will recollect that from the vernal equinox to 
the summer solstice the declination is north and increasing ; 
from the summer solstice to the autumnal equinox, north and 
decreasing; from the autumnal equinox to the winter solstice, 
south and increasing; and from the winter solstice to the 
vernal equinox, south, and decreasing ; moreover, that longi- 
tude and right ascension, are reckoned from the vernal equi- 
nox> completely round, that is, 360°. The preceding exam- 
ples are comprised in the first quadrant, from the vernal equi- 
nox to the summer solstice. For examples in the se«ond 



338 ASTRONOMICAL PROBLEMS. 

quadrant, E would be regarded as the autumnal equinox, and 
ED and EA would have to be subtracted each from 180°, 
and the remainders would be, respectively, the corresponding 
right ascension and longitude. 

In the third quadrant, viz.: from the autumnal equinox to 
the winter solstice, E would be regarded as the autumnal 
equinox, and ED and EA, being added, respectively, to 180°, 
the sums would be the right ascension and declination. In 
examples in the fourth quadrant, viz. : from the winter solstice 
to the autumnal equinox, E would be the vernal equinox, and 
the right ascension and longitude would be found by subtract- 
ing ED and EA from 360°. These facts will be evident by 
the inspection of figure 20. 

Prob. The sun's right ascension being 243° 44' 36", and 
its declination 21° 16' 4"; what is its longitude? 

The right ascension being more than 180°, shows that the 
problem is in the third quadrant, and 243° 44' 36" — 180= 
63° 44' 36 "=ED. The value of EA, as found by Napier's 
rule, is 65° 39' 10", which, added to 180°,=245° 39' 10", 
which is the answer. 



ASTRONOMICAL PROBLEMS. 339 

Given, the latitude of the place of observation, and the sun's 
declination, to find the time of its rising and setting. 




In figure 2, let the circle NPMOE be the meridian of 
the place, HO the horizon, and EQ the equator. P is the 
elevated pole of the heavens, and S the place of the sun 
when on the horizon. MSN the apparent path the sun 
describes between midnight and noon, for it is evident that 
when the sun is at N it is noon, and when at M, on the 
meridian below, it is midnight. DS is the sun's declination. 
Now in the right-angled spherical triangle PSH, right-angled 
at H, there are given the latitude, PH, (Art. 57,) and PS, the 
co-declination, to find the hour angle SPH, which, reduced to 
time, shows how long the sun takes to pass in its apparent 
course, M to S. 

Then by Napier's rule, RxCos. SPH=Tang. PHXCot. 
PS or Tang. DS. 

Prob. 1. At what time does sunrise occur at Fort Leav- 
enworth, N. Lat. 39° 21' 14", when the sun's declination is 
15° 50 North? 

R., 10.000000 

Tang. 15° 50', 9.452706 

Tang. 39° 21' 14", 9.913847 

Cos. SPH, 76° 33' 06", 9.366553 



340 ASTRONOMICAL PROBLEMS. 

Dividing 76° 33' 06" by 15, (Art. 91,) to obtain the time, 
we have 5h. 6m. 12s. for the time of sunrise. Subtracting 
this time from 12 hours gives 6h. 53m. 47.6s. for the time 
from sunrise to noon, and also the time of sunset. 

Prob. 2. What is the length of the day at Yorktown, Va., 
N. Lat. 37° 13'. when the declination of the sun is 19° 20' 10" ? 

Ans., 14h. 3m. 39.2s. 



To find the altitude and azimuth of a star when it is six hours 
from the meridian, its declination, and the latitude of the 
place of observation being known. 




In figure 3, let S be the star, P the pole of the heavens, 
Z the zenith of the place, and QL the equator — PZH is a 
meridian, PSE an hour circle, and ZSD a vertical circle. 
As the star is six hours from the meridian, ZPS is a right 
angle, and the circle PSE cuts the horizon in the east and 
west points; PER is the latitude of the place, and ES is the 
declination of the star. 

Then by Napier's rule we have in the right-angled spher- 
ical triangle, SED, RxSin. SD (altitude) = Sin. SEDX 
Sin. £E; and RxCos. SED=Cot. SEX Tang ED (ampli- 
tude) .90° — amplitude=azimuth. 



ASTRONOMICAL PROBLEMS. 341 

Prob. 1. Find the altitude and azimuth of the star Cas" 
tar, at Toronto, N. Lat. 43° 39 35", when it is six hours from 
the meridian, its declination being 32° 12' 10". 

Cot. 32° 12 10", 10.200796 

R., 10. 

Cos. 43° 39 35", 9.859410 

Cot. of azimuth or Tang ED, ampli- 
tude (65° 30' 16"), 9.658614 

A ' (Azimuth, 65° 30' 16". 
Ans * \ Altitude, 21° 35' 13". 

Prob. 2. At Knoxville, Tenn., N. Lat. 35° 59', the decli- 
nation of the sun being 20° 20', what is its azimuth and alti- 
tude at 6 o'clock in the evening? 

A (.Azimuth, 73° 18' 29". 
iLns * \ Altitude, 11° 46' 50". 

Prob. 3. In N. Lat. 42° 50', the altitude of the sun, at 
6 o'clock in the morning, was found to be 15° 25', what was 
its azimuth and declination? 

A (Azimuth, 72° 41' 45". 
Ans * X Declination, 23° 01' 03" 



If a star is on the prime vertical, its altitude and hour angle 
may he obtained, when its declination, and the latitude of 
the place is known. 




In figure 4, let S be the star, P the pole of the heavens, 
HZPR a meridian, PS an hour circle, ZSE the prime verti- 



342 ASTRONOMICAL PROBLEMS. 

cal, and HER the horizon. Then, in the spherical triangle 
ZPS, the angle SZP is aright angle. PS is the co-declina- 
tion, and PZ the co-latitude, both known quantities. 

We have, therefore, by Napier's rule, RxCos. ZPS (hour 
angle) = Cot. SPxTang ZP ; and RxCos. SP=Cos. ZSX 
Cos. PZ. ZS=co-altitude. 

Prob. 1. Find the altitude and hour angle of Arcturus, 
when exactly west of an observer at Montreal ; the declina- 
tion of the star being 19° 56' 10" North, and the latitude of 
the place 45° 31 North. 

For the altitude. 

Sin. 43° 31', 9.853366 

R., 10. 

Sin. 19° 56' 10", 9.532719 

Sin. of altitude or Cos. of co- 
altitude (28° 32 58 ), 9.679353 

. I Altitude, 28° 32' 58". 
Ans " { Hour angle, 69° 7' 53". 

Prob. 2. Find the altitude and hour angle of Markab, 
when east of an observer at Alexandria, Va., the declination 
of the star being 14° 25 50", and the latitude of the place 
38° 49'. 

A ( Hour angle, 71° 20 45". 
Ans " I Altitude, 23° 25' 34". 



Application of Kepler's third law, that the squares of the peri' 
odic times are as the cubes of the distances. 

In calculations founded upon this rule it is convenient to 
take for two terms of the proportion the periodic time of the 
earth, and its mean solar distance, calling the latter unity; 
and expressing the solar distances of other planets in multi- 
ples and fractions of this. 

The length of the siderial year in mean solar days is 
365.256374417. 

The logarithm of 365.256374417 is 2.5625978. 



ASTRONOMICAL PROBLEMS. 343 

Given, the earth's periodic time and solar distance, and also 
the solar distance of a planet, to find the periodic time or 
sideria» revolution of the latter. 

Prob. 1 If the mean solar distance of Ceres is 2.765765, 
(calling the earth's solar distance l,)\vhat is her periodic time? 

* 3 

1 ; . 365.256374417 : : 2.765765 : **^$&SSP* 
By Logarithms, 

l 3 Log. 0.0000000 



365.2563&C Log. 5.1251956 

3 

2.765765 Log. 1.3254450 

2 J 6.4506406 Lo ^^ •' * 

3.2253203 L°g- ot periodic time. 

Ans., 1680 days. 

Prob. 2. If the mean solar distance of Hygeia is 3.149384, 
what is her periodic time ? 

Ans., 2041.4 days. 

Prob. 3. If the mean solar distance of Aniphitrite is 
2.546297, what is her periodic time? 

Ans., 1481 days. 

Prob. 4. If the periodic time of Flora is 1193 days, 
what is her distance from the sun? 

Ans., 2.201 times the earth's solar distance. 

Prob 5 If the periodic time of Jupiter is 4332.6 days, 
whai. ii his distance from the sun? 

A f 5.2012 times the earth's solar distance, 
Ans *' J or 476,871,086 miles. 

Prob. 6, If the periodic time of Venus is 224.7 days, 
what is her solar distance ? 

Ans., 66,318,380 miles. 



344 



ASTRONOMICAL PROBLEMS. 



To find the distance of a heavenly body from the earth, when 
its horizontal parallax and the radius of the earth are 
known. 

(5) 




In figure 5 let S represent a heavenly body, and E the 
earth, SE a line drawn from the centre of the heavenly body 
to the centre of the earth, and SL a line drawn from the cen- 
tre of the body to the surface of the earth, tangent to it at 
the extremity of the earth's radius, EL. Then in the right- 
angled triangle, SLE, right-angled at L, we have given the 
side LE, and also the angle LSE, the horizontal parallax of 
the body, (Art. 94,) to rind the distance SE, which is obtained 
by the following proportion. Sine of the horizontal parallax 
(sine LSE) :the semi-diameter of the earth (LE) :: radius: 
the distance (SE). 

Prob. 1. What is the distance of the sun from the earth, 
its horizontal parallax being 8".9, and the earth's semi-diam- 
eter 3956.2 miles? 

Ans., 91,684,820 miles. 

Prob. 2. If the moon's horizontal parallax is 57', and the 
radius of the earth 3956.2 miles, what is her distance from 
the earth? 

Ans., 238,616 miles. 



ASTRONOMICAL PROBLEMS. M5 

To find the diameter, in miles, of a heavenly body, when its 
apparent diameter and distance from the earth are known. 




If in figure 6, S represents the heavenly body, and E 
the earth, and EL and ES two lines drawn from the cen- 
tre of the earth to the surface and centre of the body, then 
as SE is a tangent, we have a right-angled triangle, SLE, in 
which the angle LSE is a right angle, the line LE the distance 
between the two bodies, and the angle LES is the apparent 
semi-diameter of the body. From these quantities the line 
SL can be found by the following proportion. 

It: the distance (LE) ::the sine of the semi-diameter (sine 
of LES) : SL. 

Prob. 1. If the mean distance of the sun from the earth 
is 91,684,820 miles, and its apparent semi-diameter 16' 2", 
what is the extent of his diameter in miles ? 

Ans., 855,236 miles. 

Prob. 2. If the average distance of the moon from the 
earth is 238,650 miles, and her apparent semi-diameter 
15' 40", what is the extent of her diameter in miles? 

Ans., 2175.2 miles. 



Prob. 3. If Jupiter, at his conjunction, is 593.200,000 
miles from the earth, and his apparent diameter is 30", what 
is the extent of his diameter in miles ? 

Ans., 86,305 miles. 

A movable planisphere of the heavens has been constructed 
by Mr. Henry Whitall, of New York, which is an excellent 
substitute for a celestial globe, and can be furnished at a mere 
fraction of the cost of the latter. A great number of impor- 
tant problems in astronomy can be solved by it with facility, 
and to one who wishes to study the starry heavens, it will be 
of the greatest use. 



APPENDIX 



i. 

ROTATION OF THE EARTH PROVED BY THE PENDULUM. 

If a heavy weight is suspended from a point by a 
fine wire and made to vibrate as a pendulum, it will 
continue to oscillate in the same plane until it comes 
to rest, and this will be true whether the point is fixed 
or has a slow motion around a vertical axis. Imagine 
such a pendulum to be suspended over one of the poles 
of the earth, where the direction of gravity is perpen- 
dicular to the plane of the earth's rotation, and made 
to vibrate. All its vibrations will necessarily take 
place in the same plane, but during their continu- 
ance, the earth rotates on its axis from west to east 
beneath this plane at this rate of 15° an hour, and if a 
person were watching the pendulum, the plane of its 
oscillation would appear to rotate in an opposite di- 
rection, viz: from east to west, and at the same rate, 
since the spectator would be unconscious of his own 
motion of rotation with the earth. 

At the equator, where the direction of gravity coin- 
cides with the plane of the earth's rotation, the plane 
of vibration of the pendulum appears unchanged. At 
points between the equator and poles the direction of 
gravity is oblique to the plane of rotation, and the 
rate of the apparent motion of the plane of vibration 
depends upon the amount of this obliquity, being as 
the sine of the latitude. At Providence, R. I., the 
hourly motion of the plane of vibration is 10°. 

When the experiment is carefully conducted, the 
observed and computed rates of motion are very nearly 
the same, and thus a direct proof of the earth's rota- 
tion is obtained. 



APPENDIX. 347 

II. 

DENSITY OF THE EARTH. 

The mean density of the earth has been determined 
by three independent methods. 

First, by comparing the attraction of the earth with 
that of a mountain whose average density is known. 
In 1774, the Astronomer Royal, Dr. Maskelyne, as- 
certained the mean density of the earth according to 
this method, by observations on the mountain Sche- 
hallien in Scotland. Two stations were taken 4,000 
feet apart, one on the north side of the mountain, and 
the other on the south side, and nearly in the same 
meridian. A plumb line was suspended at each sta- 
tion, and the inclination of these lines observed. Their 
inclination due to the attraction of the earth alone was 
41", but their observed inclination was 53". The dif- 
ference of 12" was therefore due to the attraction of 
the mountain. The mountain having been thoroughly 
surveyed and its mass computed, it was inferred that 
this deviation would have been 21" had the mountain 
been as dense as the earth. The density of the earth 
was therefore greater than that of the mountain in the 
ratio of 21 to 12. The density of the mountain was 
found by repeated experiments to be about 2.75 times 
greater than that of water. The earth has, therefore, 
according to this method, a mean density of 4.81. 
Similar experiments, made in Edinburg in 1855, give 
a mean density of 5.32. 

A second method of determining the average den- 
sity of the earth consists in comparing the amount of 
attraction produced on a small body by a mass of 
known size and density,. with the amount of attraction 
exerted by the earth on the same body. This exper- 
iment was made by Henry Cavendish, in the year 
1798, and in the following manner : A slender rod six 
feet long was suspended at the middle by a very fine 
wire 40 inches long, and a leaden ball about two inches 



348 APPENDIX. 

in diameter was hung at each end of the rod. The 
balanced rod, after vibrating a while, came to a state 
of rest. Two spheres of lead, eight inches in diam- 
eter, were then brought near the small balls on oppo- 
site sides, when the latter were attracted toward the 
large spheres. A series of experiments was thus 
made, and the average deviation noted. 

Having obtained the amount of this deviation as a 
basis, the amount of attraction which would be exerted 
on the small balls by spheres of lead as large as the 
earth could be readily computed. Now the amount of 
attraction exerted by the earth on the small balls is 
known, for it is simply their weights, and the density 
of lead is also known. Three terms of a proportion 
are therefore given, from which the fourth, viz : the 
density of the earth, can be found. The result ob- 
tained by Cavendish was 5.45. 

Experiments similar to those of Cavendish were 
made in Saxony, by Dr. Reich, in 1836, and also in 
England, by Sir Francis Baily, in 1841 and 1842. 
Baily, from the results of two thousand trials, deter- 
mined the mean density of the earth to be 5.67. 

A third method of ascertaining the mean density of 
the earth is derived from the variation in the rate of 
vibration of a pendulum on the surface of the earth 
and at the bottom of a deep mine. The number of 
vibrations which a pendulum will make in a given 
time, as one hour, depends upon the amount of the 
force of gravity. The rate of vibration is therefore a 
measure of the intensity of the earth's attraction. At 
the surface of the earth the pendulum is attracted by 
every atom of matter in the globe, but at a point be- 
low the surface it vibrates, as mathematicians have 
shown, only by the attraction of such a portion of the 
earth as is represented by a sphere whose radius is the 
distance from the point to the centre of the earth. 
For instance, if the number of vibrations of a pendu- 
lum during an hour is noted at the top of a mine 
2,000 feet deep, and also at the bottom, the first rate 



APPENDIX. 349 

is a measure of the attraction of the whole globe, and 
the second of an interior sphere, having a radius 2,000 
feet less than that of the earth ; the spherical shell 
2,000 feet in thickness producing no effect on the 
pendulum at the bottom of the mine. The difference 
in the two rates of vibration affords the means of as- 
certaing the amount of the attraction of the spherical 
shell. The volume of the earth is known, that of the 
spherical shell can be computed, and its approximate 
density may be obtained by an examination of the na- 
ture of the strata which have been pierced in sinking 
the mine. From these data the mean density of the 
earth can be determined. 

Experiments of this kind were made by Prof. Airy, 
the Astronomer Royal of England, and other eminent 
men of science, in 1854, in a shaft of the Horton col- 
liery, 1,260 feet deep, and they arrived at the conclu- 
sion that the mean density of the earth was 6.565. 
In an analogous manner, the mean density of the 
earth has been computed in Italy, by comparing the 
rates of vibration of a pendulum on Mount Cenis, and 
at the sea-level. The mean density deduced from 
these experiments was 4.84. 

An average of the various reliable results which 
have been obtained, makes the mean density of the 
earth about 5.44 times greater than that of water. 



850 



APPENDIX. 



III. 



TABLE OF KNOWN PLANETOIDS. 

FROM THE LATEST AUTHORITIES IN THE ORDER OF DISCOVERY. 
In the solar distances, the distance of the earth from the sun is taken as unity. 







i 


6 

1- 


>>o 








Symbol. 


Name. 


s 
1 


imeters 
aaputed b 
b formula 
gelander. 


When 
Discovered. 


Discoverer. 








38S-3 








(1) ? 


CERES,. 


2.766 1680 




1801, Jan. 


1, 


Piazzi. 


(2) » 


PALLAS, . 


2.769 j 1684 




1802, Mar. 


28, 


Olbers. 


(3) 5 


JUNO, . 


2.676 1592 


105 


1804, Sept. 


1, 


Harding. 


(4) ft 


VESTA, . 


2.360 


1325 




1807, Mar. 


29, 


Olbers. 


(5) 


ASTREA, 


2.577 


1511 


60 


1845, Dec. 


8, 


Hencke. 


(6) 


HEBE, 


2.424 


1380 


97 


1847, July 


1, 


Hencke. 


(7) 


IRIS, . 


2.336 


1346 


97 


1847, Aug. 


13, 


Hind. 


(8) 


FLORA, . 


2.201 


1193 


62 


1847, Oct. 


18. 


Hind. 


0) 


METIS,. -. 


2.386 


1346 


75 


1848, Apr. 


25, 


Graham. 


(10) 


HYGEIA, . 


3.151 


2041 


112 


1849, Apr. 


12, 


Gasparis. 


(11) 

(12) 


PARTIIENOPE, . 


2.451 


•1403 


62 


1850, May 


13, 


Luther. 


VICTORIA, or CLIO, 


2.334 


1301 




1850, Sept. 


13, 


Hind. 


(13) 


EGERIA, 


2.577 


1510 


70 


1850, Nov. 


2, 


Gasparis. 


(14) 


IRENE, . 


2.586 


1522 


67 


1851, May 


20, 


Hind. 


(15) 


EUNOMIA, . 


2.644 


1570 


115 


1851, July 


29, 


Gasparis. 


(16) 


PSYCHE, . 


2.923 


1825 


215 


1852, Mar. 


17, 


Gasparis. 


(17) 


THETIS, 


2.473 


1421 


37 


1852, April 


17, 


Luther. 


(18) 


MELPOMENE, . 


2.295 


1271 


52 ' 


1852, June 24| 


Hind. 


(ly) 


FORTUNA, . 


2.4416 


1393 


60 


1852, Aug. 


22, 


Hind. 


(20) 


MASSILTA, 


2.414 


1366 


67 


1852, Sept. 


19. 


Gasparis. 


(21) 


LUTETIA, . 


2.441 


1388 


40 


1852, Nov. 


15, 


Goldschmidt. 


(22) 


CALLIOPE, 


2.909 


1440 


50 


1852, Nov. 


16, 


Hind. 


(23) 


THALIA, 


2.628 


1567 


40 


1852, Dec. 


15, 


Hind. 


(24) 


THEMIS, . 


3.143 


2042 


35 


1253, April 


5, 


Gasparis. 


(25) 


PHOCCEA, . 


2.401 


1359 


35 


1853, April 


6. 


Chacornac. 


(26) 


PROSERPINE, . 


2.656 


1581 


40 


1853, May 


5, 


Luther. 


(27) 


EUTERPE, 


2.347 


1314 


37 


1853, Nov. 


8, 


Hind. 


(28) 


BELLONA, 


2.778 


1689 


60 


1854, Mar. 


1, 


Luther. 


(29) 


AMPHITRITE, . 


2.554 


1492 


82 


1854, Mar. 


1, 


Marth. 


(30) 


URANIA, . 


2.365 


1328 




1854, July 


22, 


Hind. 


(31) 


EUPHROSYNE, . 


3.151 


2048 


50 


1854, Sept. 


1, 


Ferguson. 


(32) 


POMONA, . 


2.586 


1522 


32 


1854, Oct. 


26, 


Goldschmidt. 


(33) 


POLYHYMNIA, . 


2.865 


1773 


35 


1854, Oft. 


28, 


Chacornac. 


(34) 


CIRCE, 


2.686 


1610 


22 


1855, April 


15, 


Chacornac. 


(35) 


LEUCOTHEA, 


3 004 


1880 


22 


1855, April 


19, 


Luther. 


(36) 


ATALANTA, . 


2.746 


1665 


20 


1855, Oct. 


5, 


Goldschmidt. 


(37) 


FIDES, . 


2.641 


1568 


45 


1855, Oct. 


5, 


Luther. 


(38) 


LED A, 


2.740 


1656 


37 


1856, Jan. 


12, 


Chacornac. 


(39) 


L^ITITIA, . 


2.774 


1683 


122 


1856, Feb. 


8, 


Chacornac. 


(40) 


HARMONIA, . 


2.678 


1247 


100 


1856, Mar. 


31, 


Goldschmidt. 


(41) 


DAPHNE, . 


2.766 


1358 


42 


1856, May 


23, 


Goldschmidt. 


(42) 


ISIS, . 


2.440 


1387 


25 


1856, May 


23, 


Pogson. 


(43) 


ARIADNE, . 


2.203 


1195 




1857, April 


15, 


Pogson. 


(44) 


NYSA, 


2.423 


1384 


42 


1857, May 


27, 


Goldschmidt. 


(45) 


EUGENIA, . 


2.721 


1659 


27 


1857, June 


27, 


Goldschmidt. 


(46) 


HESTIA, . 


2.526 


1479 


15 


1857, Aug. 


16, 


Pogson. 


(47) 


AGLAIA, . 


2.881 


1476 


37 


1857, Sept. 


15, 


Luther. 


(48) 


DORIS, . 


3.109 


2000 


52 


1857, Sept. 


19, 


Goldschmidt. 


(49) 


PALES, . 


3.082 


1980 


37 


1857, Sept. 


19, 


Goldschmidt. 


(50) 


VIRGINIA, 


2.649 


1577 


20 


1857, Oct. 


4, 


Ferguson. 



APPENDIX. 



351 





TABLE OF PLANETOIDS.— (Continued.) 








w 


1 

.2 °° 
§ 5? 








Symbol. 


Name. 


m 

ft 


Ills 

S a ® go 


When 
Discovered. 


Discoverer. 






O 
03 




S85-5 






(51) 


NEMAUSA, . 


2.366 


1339 




1858, Jan. 22, 


Laurent. 


(52) 


EUROPA, . 




3.100 


1992 




1858, Feb. 4, 


Goldschmidt. 


(53) 


CALYPSO, . 




2.619 


1543 




1858, April 4, 


Luther. 


(54) 


ALEXANDRA, . 




2.712 


1642 




1858, Sept. 11, 


Goldschmidt. 


(55) 


PANDORA, . 




2.959 


1692 




1858, Sept. 11, 


Searle. 


(56) 


MELETE, . 




2.596 


1517 




1857, Sept. 9, 


Goldschmidt. 


(57) 


MNEMOSYNE, 




3.156 


2049 




1859, Sept. 22, 


Luther. 


(58) 


CONCORDIA, . 




2.701 


1615 




1860, Mar. 24, 


Luther. 


(59) 


OLYMPIA, . 




2.713 1632 




1860, Sept. 12, 


Chacornac. 


(60) 


ECHO, 




2.393; 1351 




1860, Sept. 15, 


Ferguson. 


(61) 


DANAE, 




2.983 1902 




1860, Sept. 19, 


Goldschmidt. 


(62) 


ERATO, . 




3.130 2024 




1860, Oct. 10, 


Forster. 


(63) 


AUSONIA, . 




2.3951355 




1861, Feb. 10, 


Gasparis. 


(64) 


ANGELINA, . 




2.680 11603 




1861, Mar. 2, 


Tern pel. 


(65) 


CYBELE, . 




3.42012322 




1861, Mar. 4, 


Tempel. 


(66) 


MAI A, 




2.663 1579 




1861, April 9, 


Tuttle. 


(67) 


ASIA, . 




2.422 


1371 




1861, April 17, 


Pogson. 


(68) 


LETO, 




2.783 


1641 




1861, April 29, 


Luther. , 


(69) 


HESPERIA, . 




2.971 


1957 




1861, April 29, 


Schiaparelli. 


(70) 


PANOP.EA, 




2.613 


1594 




1861, May 5, 


Goldschmidt. 


(71) 


NIOBE, . 




2.750 


1671 




1861, May 29, 


Peters. 


(72) 


FERONIA, 




2.265 


1148 




1861, Aug. 13, 


Luther. 


(73) 


CLYTIA, 




2.666 1594 




1862, April 8, 


Tuttle. 


(74) 


GALATEA, 




2.778 1509 




1862, Aug. 29, 


Tempel. 


(75) 


EURYDICE, . 




2.6711 1570 




1862, Sept. 22, 


Peters. 


(76) 


FREYA, . 




2.386 2080 




1862, Oct. 21, 


D 'Arrest. 


(77) 


FRIGGA, . 




•2.673 1595 




1862, Nov. 12, 


Peters. 


(78) 


DIANA, . 




2.6231677 




1863, Mar. 15, 


Luther. 


(79) 


EURYNOME, 




2.443 


1397 




1863, Sept. 14, 


Watson. 


(80) 


SAPPHO, . 




2.297 


1272 




1864, May 2, 


Pogson. 


(81) 


TERPSICHORE, 




2.859 


1766 




1864, Sept. 30, 


Tempel. 


(82) 


ALCMENE, 




2.755 1670 




1864, Nov. 27, 


Luther. 


(83) 


BEATRICE, . 




2.429! 1382 




1865, April 26, 


Gasparis. 


(84) 


CLIO, 




2.367(1330 


52 


1865, April 25, 


Luther. 


(85) 


IO, 




2.654J1579 




1865, Sept. 19, 


Peters. 


(86) 


SEMELE, . 




3. 112! 2005 




1866, Jan. 4, 


Tietjen. 


(87) 


SYLVIA, 




3 494 2385 




1866, May 16, 


Pogson. 


(88) 


THISBE, . 




2.769 


1682 




1866, June 15 x 


Peters. 


(89) 


JULIA, . 




2.550 


1486 




1866, Aug. 6, 


Stephan. 


(90) 


ANTIOPE, 




3.137 


2029 




1866, Oct. 1, 


Luther. 


(91) 


J3GINA, 




2.492 


1437 




1866, Nov. 4, 


Stephan. 


(92) 


UNDINA, . 




3.192 


2083 




1867, July 7, 


Peters. 


(93) 


MINERVA, . 




2.756 


1679 




1867, Aug. 24, 


Watson. 


(94) 


AURORA, . 




3.160 


2052 




1897, Sept. 6, 


Watson. 


(95) 


ARETHUSA, 




3.069 


1964 




1867, Nov. 23, 


Lutber. 


(96) 


JEGLE, 




3.054 


1950 




1868, Feb. 17, 


Coggia. 


(97) 


CLOTHO, . 




2.669 


1592 




1868, Feb. 17, 


Tempel. 


CggJ 


IANTHE, . 




2.685 


1603 




1868, April 13, 


Peters. 


,i$ 


DIKE, . 










1868, May 28, 


Borelly. 


(100) 


HECATE, . 




2.994 


1892 




1868, July 11, 


Watson. 


(101) 


HELENA, . 




2 573 


1508 




1868, Aug. 15, 


Watson. 


(102) 


MIRIAM, . 




2.662 1587 




1868, Aug. 22, 


Peters. 


(103) 


HERA, . 




2.702! 1622 




1868, Sept. 7, 


Watson. 


(104) 


CLYMENE, 




3.180|2071 




1868, Sept. 13, 


Watson. 


(105) 


ARTEMIS. . 




2.380 ■ 1341 




1868, Sept. 16, 


Watson. 


(106) 


DIONE, . 




3.2012092 




1868, Oct. 10, 


Watson. 


(107) 


CAMILLA, . 








1868, Nov. 17, 


Luther. 


(108) 


HECUBA, . 




3.19012081 




1869, April 2, 




(109) 


FELICITAS, . 




2.678 1601 




1869, Oct. 9, 


Peters. 


(HO) 


LYDIA, . 




1 




1870, April 19,'Borelly. * 



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